A method is simply a function that's in a class. The term applies to OOP in any language. Since Java requires that everything be a class all functions are automatically methods (to oversimplify it).
What methods you put in a zombie class depends entirely on how you want your game to work, but aside from the constructors (you'll read about those) some obvious possible candidates are draw(), setPosition(), setPatrolRoute(), takeDamage(), attackPlayer(), and maybe takeDamage() will call a private function like explode() if it discovers the zombie lost its last HP, etc etc. And later on you might find yourself duplicating these functions in several enemy classes so instead you might make a base class called Enemy and have each class inherit from that. We could go on and on.
By the way, Java's OOP really isn't that different from C++'s OOP, so you'll see a lot of other terminology that carries over. The biggest differences I know of offhand is that Java adds Interfaces (in C++ terms these are like abstract classes with no concrete parts) because that provides a simple solution for multiple inheritance in the rare cases you need it, and C++ has a bunch of extra features Java doesn't like operator overloading and templated everything and god knows what else (and C++11 added even more!). That probably sounds like gibberish now, but it'll make sense eventually.