How can I check automatically what is seen and what not? Or at least, how can I organize some partly automatic tests?

IDE: Eclipse (could use also IntelliJ Idea if necessary)

Testing tool: Junit (again, could use something else if advised, but free only)

Application OS: Android

Developer's OS: Linux

Language: Java

The application is a user wrapper for the firmware TV player, called as external activity. So, 70% of the code is for GUI. (The other 30% speak to servers and provides info to the GUI)

Before I programmed the testing function myself, not using any tools. Now I have a tool at hand. But I can't imagine how could I test the UI, with the tool or without it. (Strictly said, with the Internet connections I have problems too, but I'll leave them probably for the other question.) I need the very principles, so the answer needn't be too platform-dependent.

Of course, it is good to check, is some element in another and checked or not. Some regression checks would be nice for that. But I should also be sure that the element mentioned is not cut by some other elements and winks as I ordered by animation.