I am planning to create an indie game using Java and Eclipse IDE and I want to put the finished product to Steam Greenlight.
How does the whole process work after the game is finished and running only on Eclipse?
I assume you really want to know two things:
The answer to #1 is "yes." Steam hosts other Java games (like Spiral Knights).
For #2, I suggest you package your game using launch4j. This will provide you with native (Windows, Linux) wrappers around your application. Other benefits include (from their home page):
You can get the latest version from Maven for your maven/gradle builds.
Also, note: Greenlight is not some magic marketing machine. You have to market your game really, really well to get it greenlit.
If your game is running only on Eclipse, start by packing the .jar, the assets and all that come with your game and try your game on different OS (or ask other people to do it).
You will have a good return about the technical problems ("game's not working", "laaag") and the gameplay problems ("not funny enough", "what am I supposed to do ?", "boring...").
Then you have to pay a fee, for the Greenlight submission.
In my opinion it is even better if you have a native launcher, but that is a bonus.