Finding all solutions for diophantine equations

Hi, this is my first post here. I'm taking a discrete mathematics course in University and it's kicking my ass. I'm not good at math and the professor barely speaks english, not a good combination. So this is probably the first of many questions I'll be asking here. I hope that you'll be patient with me as long as I show that I really am trying to learn this stuff.

How do you find all solutions for a diophantine equation? Currently I only know how to find a single solution, and after that it gets a little fuzzy.

This is what I know:

1)find gcd(a,b) *using Euclidean Algorithm

2)Use extended/reverse Euclidean Algorithm to solve for x and y

3)?....

Thanks for your help!