People seem hesitant to answer this, and I'm not quite sure why.
A method is a set of code that is defined as part of a class. It performs some task, and optionally returns a value. It generally operates on class or instance variables.
A class is a set of methods and variables. This is used to encapsulate related data and actions on that data. Often this is used to model a real-world item like a car, shape, or animal.
An instance or Object refers to a concrete example of a class. These are the foundation of Object-Oriented Programming. Where a class is like a plan or idea, an object is a single item that is built from that plan. For example, a single German shepherd named Brüno.
A method is most commonly used to act on an object/instance such as "walk" or "call" on a dog. This is called an instance method. There are methods that act on a class, such as "getPhylum" on the dog class. These are called class methods.
Variables can also be tied to a class or instance. For example, the dog class might have a class variable to hold it's phylum, or return a list of all dog instances you've created. An instance variable would hold information about one single dog, like it's name, breed, etc.
-Lee