To be honest, I think you're way off. All the right terms are there but you seem to be miss-using them.
Think of a class as a template. It's not an actual thing but it describes the common features of all instances of that thing. So if you have a class called Dog it's not a dog but it has place holders (attributes) for all the things you might need to record to describe a dog. It says that dogs have names, a breed, an owner and a current level of excitement. It also has methods which describe the things that all dogs do and how they do them. So it has a method called bark and wag tail. These methods will be shared by all instance (see below) of the class Dog.
An object is an instance of a class. E.g. Spot. Spot's name is... well... Spot, his owner is Jason, his breed is cocker Spaniel and he's currently feeling a little frisky. So by assigning values to the various attributes of a Dog Class, we can describe Spot. And because Spot is an instance of Dog he can bark and wag his tail (because a Dogs methods are shared by all instances of Dog).
Methods are the things we write in a class in order to describe how instances of that class should do things. So to bark a dog must open it's mouth, suck in some air, and then exhale it sharply to vibrate it's vocal chords. All dogs use the same basic mechanism for barking so we can write this method once, in the Dog class, and then all instances of Dog will bark in the same way.
A function is a just type of method. It's a method that returns a value. So you might want to be able to tell how old a dog is. That would be a case of subtracting it's date of birth from todays date. So you'd write a method called Age which would do the maths and return the result. The corollary of functions are procedures. These are methods which don't return a value. So bark and wag tail would be procedures rather than functions.
Public and Private are just to do with where a particular method or attribute can be accessed from. A private method or variable can only be called from the object it belongs to. So Bark and Wag Tail would probably be private methods - only Spot can decide whether he's excited enough to bark and wag his tail. Public methods and attributes are visible outside the object. So you might implement a method called Encourage which a dogs owner can call. The method would check if the dog was excited enough and, if so, would in turn call the private Bark and Wag Tail methods. Note that the owner can't wag Spot's tail or bark for him, but he can encourage Spot to bark and wag his own tail.
