The compiler in Eclipse runs automatically. It even runs while you type, although to be sure about your errors, save all of your files. Don't try to run anything, though.
Your errors can be found in the Problems window at the bottom of the Eclipse screen. If you double click on an error there, it will take you immediately to the line with the error in it.
It's best if there are no warnings in that window either. Some of them might be temporary (i.e., you've declared a variable without using it yet), others might be because I've asked you to write strange code. As you instructor to help get rid of the warnings, too, since they can cause problems later on.