I found a few code examples, but I don't know with which JNA versions I can use which methods. I did only find snippets, where classes were missing and I wasn't able to import them.
I would like to know which JNA version I should use and how to get a screenshot as BufferedImage.
A list of required imports would also be great.
It looks like there are several examples at this link. I'll discuss one below (#3) for discussion purposes, but you may find one of the other examples more applicable to your situation and hopefully this answer will help you understand the process.
Before the example, I will answer your question "which JNA versions"... you should use the latest version in almost all cases. JNA is a user-supported library, and the core JNA code doesn't change much but each new version adds more user-contributed mappings to native functions. Note their FAQ question, "JNA is missing function XXX in its platform library mappings" and the answer, "No, it's not, it's just waiting for you to add it :)". If the mapping you need is not in JNA, you can simply add it using the example provided, for your immediate needs. Better yet, contribute your mapping to the JNA project so that the next person in your situation will benefit from the work you've done!
Now, example #3 from the link takes a screenshot of the entire screen and returns it as a BufferedImage object. The full source code for that example shows all the imports you will need, most from JNA's WinGDI class.
If you scroll to the bottom of the class you may also see that the authors have extended two JNA platform interface contributions with mappings that aren't in JNA (or weren't in 2010 when that code was written). You will have to do similar mappings (and perhaps contribute them to their respective JNA classes when you're done).