WOULD: Is usually used when explaining something you did/didn't do or do/don't do. ("would/wouldn't do ____") It is also used to give someone your opinion or to express a desire. Its hard to explain without using the word, so here are some examples:
"I would have gone to the store today, but my car wouldn't start."
"I would like to walk in the park today."
"There wouldn't be a problem if you had been more polite."
"I would study more for that test if I were you."
WILL: Is used mainly to state something that is definitely going to happen or expected to happen. Also, possibly used in an order (final example).
"I will go to the store today after I get my car fixed."
"I will go for a walk in the park today."
"There will be a problem if you aren't more polite."
"You will study more for that test!"
WILL can also be used as a word to express someone's determination ("will power"), desire, or orders.
"John lost his legs in the war, but he maintained a will to live on."
"All the members of government bent to his will."
Hope that helps!