There are a number of different possibilities here. First off, where you get the games is up to you. If there are some with "apt-get" you can find, OK. Same thing for the internet, you just have to transfer them onto your Pi / download them there directly.
The main problem with Java games is that many depend on libraries such as LWJGL, which ARE hardware specific in a way.
So you either have to find a version of the game specifically made for the Pi, or try to patch the libs in yourself, if you believe that the Pi is powerful enough to run the game at all. Also watch out for OpenGL requirements: OpenGL-ES runs on the Pi, but FULL OpenGL only with the new experimental driver on a Pi2 and Pi3.