Well, you don't have any class and you just fired yourself to boot.
General rules:
Use .equals() when dealing with objects (String, for example)
Use == when comparing primitives (int, double, boolean, etc)
Use == to test if something is null
The last case is unusual- sometimes you need to check for null values. For example:
String name = playerMap.get("Foo");
if (name.equals("Bar"))
//stuff
That would give you a runtime error if "Foo" wasn't in the map, since it'd return null and store that in "name". A safer way to do so is this:
String name = playerMap.get("Foo");
if (name != null && name.equals("Bar"))
//stuff
If the name is null and fails the first condition, Java won't even evaluate the other half of the expression. It's called a short-circuit and is a handy way to avoid exceptions.