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Start Java EE project after standard java

My task is to make a small a project for start my ee studies. Till now, I learned standard java, but i don't get what ee means exactly, how my project would be an enterprise stuff. Has it a different syntax or different setup in IDE? I know it's not a clever question, but I really don't know where to start. Do you have any idea for start a project?

Java EE is no different language or has no different syntax than Java SE. It's built on top of Java SE and comprises a set of standardized APIs and libraries that are helpful for solving problems in an enterprise context.
To name a few:
Web Applications (Servlets, JSPs, JSF, WAR-packaging)
RESTful- and WebServices (Jax-RS, Jax-WS)
Persistence (EJB, JPA)
Context Dependency Injection (CDI)
Security
Batch
Messaging
...
Further it defines a runtime environment - an Application Server - to run enterprise applications. Nevertheless, the classic application server model has become somewhat obsolet, nowadays you either run a single application in an application server or use only parts of the libraries and APIs and embedd those in your applications.
So basically, all you need is an IDE and the libraries. When you're using maven as build environment, all you need is the java-ee maven dependency, see Maven Central
Usually you don't need to know all the libraries and APIs of Java EE in detail, it's good to know what is available out-of-the-box (so you don't reinvent the wheel), but you hardly will need all of them in all of your projects.
I personally avoid JSF, hardly have to deal with JPA, only occasionally do something with Batch or EJBs. More common are CDI, Restful or WebServices and WebApps, and usually a bit of Security.
And a good example for a Java EE Projects, a simple one with some typical use cases and very little code is Adam Bien's Guestbook2.0, which only requires Docker to run.

Java webdevelopment IDE/Server/Documentation

I have been using PHP (OOP) with various Frameworks for all my webdevelopment projects for the last few years. Next year I'll have to learn Java as part of CS university course, so I thought it may be a good idea to switch to Java for some of my smaller webdevelopment projects, so that I can get to know Java in advance.
What do I need to use Java for backend web development? What IDE/Server software/etc. should I use? What frameworks are available and which documentations could one recommend?
I know this is strictly not a Stackoverflow question, but I'd really like to hear the opinion of the very professional community here at Stackoverflow!

The web development component of Java is called Java EE. You should look into that.
As IDE you can use Eclipse, Netbeans, etc. (you can download versions that are specifically aimed at Java EE development, with bundled servers like GlassFish or Tomcat).

Use all of these technologies and learn what the terms mean: Servlet, JSP, JSTL, Filter, Tag library (create your own).
A very popular framework is Spring. Spring Core and Spring MVC has recreated most of the Java EE components but in a way that is easier to use.
The DWR library makes AJAX very easy.
Learn how to use Spring ORM, Hibernate or JPA.

I also just want to add my own answere to show what I choose in the end to work with:
IDE: NetBeans
Framework Play! Framework

How to develop Java webapps in a Ruby on Rails-like way?

We've got an app that needs to run in a Java app server. I've got to develop a webapp to go with it. I've started reading about Ruby on Rails, and I really like the approach: MVC, convention over configuration, tons of stuff taken care of for you.
I may be dreaming the impossible dream, but are there any Java webapp development frameworks out there that work in a similar way?
Straight JSP is miserable, because logic and presentation are mixed. Simple template systems, like Velocity and Freemarker don't do the database stuff. I don't know much about Spring.
Everybody here knows Java, and we don't have time before the next release cycle to learn an entirely new language and library, else I'd plunge into RoR in a serious way.

Not impossible at all. It's already been done.
Here are a few Java-equivalents:
Grails http://www.grails.org/
SpringRoo. http://www.springsource.org/roo
Spring MVC. http://www.springsource.org/
All are products of SpringSource. If you're getting serious about Java web development, I highly recommend you check them out.
Grails was actually inspired by Rails, hence the name, so you'll see many similarities in features and paradigms between the two, including MVC, convention-over-configuration, and code generation. So if you're looking to get right into Rails-like development in Java, I highly recommend Grails. I should note that Grails has more features than Rails, some of which I think Rails should adopt. An example is Grails provides a service layer to handle all business logic. You could easily implement a service layer in Rails, but its convenience we all love, and because Grails includes it, it is more convenient. I've hopped between Rails and Grails once upon a time, both great frameworks.
Keep in mind that you can do Rails development with Java as well, via JRuby, which is not a bad option either. You get all the features of the Ruby language (v. 1.8), along with the ability to integrate and use Java libraries within your Ruby code.
SpringRoo is SpringSource's new code generator framework, so you can use it with the Spring framework to aid in agile/rapid application development.
Grails is actually built on-top of the Spring framework and Groovy. Groovy is Java-derivative which looks more like a scripting language and provides all the meta/dynamic programming goodness that you see in languages such as Ruby and Python. However, Groovy allows you to write Java code as well, so there's no need to learn it, not entirely at least.

Have a good look at the the Play Framework. I think that it's the best way to develop Java web applications at the moment. Certainly the quickest. There is no deploy cycle. Save the code and refresh the browser.
It comes with Hibernate and a host of enhanced functionality that streamlines the development process. Totally REST based and stateless.
Add in jQuery and it feels like web heaven.

Starting a Java project - IDE, Framework, etc. -

I need support in order to speed up development process. I received a request to start developing a website with java technology. I usually develop in C# - ADO for Entities - ASP.NET MVC - MSSQL server - Visual Studio. Best of these choices were:
- C# Intellisense.
- ORM.
- Complete Security Management of Users, Roles.
- Separation of Concerns into MVC.
I was wondering if any can help me to determine best Java MVC Framework - DB - IDE based on these premises, Start a project with:
- Integrated security for users, roles
- MVC
To shed more light, to replicate same functionalities I can have each time I start a website using C# ASP.NET MVC 2 project. example http://nerddinnerbook.s3.amazonaws.com/Images/image020.png

First, let's discuss IDE, ORM, and security, and DB: In my opinion, the best Java IDE is IntelliJ IDEA. It's from the same folks who have developed Resharper for Visual Studio. It has the most powerful editor of all Java IDEs and has built-in support for many popular Java frameworks.
ORM: The most powerful ORM library in Java is Hibernate. Hibernate itself is an implementation of Java Persistence API (JPA) standard. EclipseLink is another implementation of JPA, but Hibernate is a better option IMO.
Security: Spring Security is probably the most powerful security (authentication and authorization) framework available in the Java world.
DB: If you are comfortable with SQL Server, then keep on using that. However don't use Microsoft's JDBC drivers. Instead use a driver from DataDirect: http://web.datadirect.com/products/jdbc/index.html. If you don't want to use SQL Server, MySQL is a great FOSS choice and Oracle, DB2, etc. are other options.
For the Web framework, there are several options:
Option 1: If you want a RAD style framework, choose Grails. Grails is similar to Ruby on Rails but uses JVM and a Java-like but dynamic language named Groovy. Grails' ORM API is called GORM, which is built on top of Hibernate, but is much easier to use. Grails also uses Spring Security for managing security.
Option 2: If you want an enterprise-grade framework, choose JBoss Seam + JavaServer Faces. JSF is a component-based MVC framework, and there are plenty of great JSF libraries available for use: RichFaces, OpenFaces, etc. Seam integrates JSF with EJB and together they make a great enterprise framework. However it has a steep learning curve.
Option 3: Use Spring + SpringMVC + JPA.
Option 4: Use Struts 2 .
Final remarks: If you are looking for an easy-to-learn MVC + ORM framework, use Struts 2 + JPA. If you are looking for a RAD and easy-to-use MVC + ORM framework, use Grails. If you are looking for a robust and enterprise-grade (but not-easy-to-learn) framework, use JBoss Seam.

Not only Spring MVC but the whole Spring eco system will get you up and running with the least surprises. You can also download the Spring Tool Suite (a preconfigured eclipse version tailored for Spring) to get an integrated development environmanet which knows about all spring stuff.
But Spring - Spring MVC - Hibernate - Spring Security and STS seems to cover your needs and will provide a sound basis to do the project without too many bad surprises. This leaves you to focus on the customer and the jump to Java.
Afterward you might consider different options in the Java space, as there are plenty of other frameworks available with their strong points. But in the short run it is better to limit the number of moving parts

The standard, most common framework/orm setup is spring/hibernate. Both of these tools have unfortunately been grown to ridiculous extremes over the years, so they may seem daunting in size, but a simple setup with each is much easier than it may seem from looking at all of the options on their respective sites.
Best suggestion would be to follow a step-by-step to get a basic spring/hibernate setup going and just expand off of that. At one point I had a prototype project like this I'd use to generate a "starter-set" to bootstrap projects.
BTW, I'd also suggest a simple ant build script. Some people may suggest maven, but it's enormous and very (imo overly) complex, and you're going to have enough new tools to wrap your head around to want to avoid having to learn another large command set.

Welcome to the Java world. The best thing (and in some cases also the worst thing) about the Java domain is that you can create your own stack based on your requirements. You're not necessarily bound to a single vendor as is commonly the case in the .NET domain.
Since it seems you're in a greenfield situation you can:
Adopt the webdevelopment stack of a large commercial vendor like Sun/Oracle (JSF/EJB3 + NetBeans/JDeveloper + Glassfish/Weblogic + MySQL/Oracle) or IBM
Adopt the webdevelopment stack of a smaller open source vendor like JBoss, SpringSource.
Take a look at JBoss Seam and SpringSource Grails and Roo (the latter two are based on the frequently mentioned Spring/Hibernate frameworks)
Mix and match your own stack based on the above and your requirements. Although this requires deep knowledge of the various technologies, frameworks, tools available.
You have lots of options as you can see. Now since your interested in a productivity focused stack - and I suspect an opensource one - and you have no legacy I recommend either Grails or Roo. In which Roo is probably the most accessible one since you don't have to learn Groovy. If you don't like the generation tooling I advice you the stick to the Spring stack and just adopt Spring/JPA/etc.

As for IDE, the only Java IDEs worth their salt IMHO are Eclipse and Netbeans, especially since both of them are free. Use Eclipse for extensibility and ease-of-use, use Netbeans if you need to rapidly develop a GUI.

Simple Java web application on Tomcat

If we only need to graphically authorize a user,
view a few tables representation (from database),
ability to change data in the database visually
what tools to use to write such a web application that will run on Tomcat?
What framework allows to do that in the most straightforward, easy-to-manage and elegant way?

I would look at Spring Roo as the framework for building your app. It will allow you quick construction of most of the features you are looking for in several minutes. (or so they claim)

There are so many elegant web frameworks available to choose from...
A JSF solution is a one suggested by the Java EE standard - if you select JSF you'll have to be more verbose in the code, but you'll have the assistance of tools such as the Visual JSF designer in NetBeans. Using JSF2 is a much better idea, IMO.
I personally recommend you to have a look at Wicket - it's a great Java web framework, centered around ideas such as ellegance, simplicity and usability.
There are many more great frameworks out there, but this is a start.

You can also try Grails. It's Java + Groovy scripting + Spring Framework + GORM + Spring Security. Less boiler plate.
Tools: Spring Source Tool Suite (Eclipse based IDE).