I'm switching over from Eclipse to IntelliJ. In Eclipse, if you do Ctrl+O in the editor, it will show a hover popup that allows you to search for a method in the class you're editing.
What is the equivalent shortcut for that in IntelliJ?
Use Navigate (View in older versions) | File Structure Popup (Ctrl+F12 on Windows, ⌘+F12 on OS X). Start typing method/symbol name to either narrow down the list or highlight the desired element. Press Enter to navigate to the selected element.