After looking at the link given by corsair, see this link too http://www.butte.edu/departments/cas/tipsheets/grammar/would.html And then give this test to check your understanding :) http://www.tolearnenglish.com/exercises/exercise-english-2/exercise-english-18159.php

Would, should and could are three auxiliary verbs that can be defined as past tenses of will, shall, and can. For more information read this: http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv43.shtml

May I add to this answer? These words are always some of the most troublesome for my adult ESL students here in the US! Would and should, along with all the other modal verbs, have multiple uses and it takes some time to learn when they are appropriate. I will address the most common usage in the present tense of the two words you asked about. In the present tense, the difference is this (used with the verb "to go" as an example"): SHOULD "I should go to the bank with him, but I might stay home and sleep." Here, "should" implies OBLIGATION to go, but not as strongly stated as when the word "must" (or the phrasal verbs of obligation: have to, need to, have got to). "Should" conveys an obligation to do something...but an obligation that the speaker might not actually fulfull! Another example: I SHOULD leave the computer and do some housework right now! But I am still sitting here.. so it's not as strong as saying, "I MUST leave the computer now!" WOULD "I would go to the bank with him, but he hasn't asked me." Here, "would" means that the person has the willingness to go, IF the situation presents itself. There is no obligation. USE IN THE PAST TENSE "Would" is used in the past tense, as corsair.kit stated in her response, but to speak of the past in a particular way -- to convey habitual or repeated actions. This usage is less common than the willingless usage I just described. In this usage, "would" is often replaced by "used to" -- "When I was a child, I would dance every day." "When I was a child, I used to dance every day." -- much more common, at least in my part of the world! :)

Okay, this is a bit difficult to explain without referring back to the actual words themselves. I will try my best. So, the word 'should' is used to recognize that there is an activity or such that needs to be done, but will not necessarily get done. It is usually used to talk about a duty, responsibility, or to present an idea. For example: "I probably should do my homework, but I'm too tired." or "We should go see a movie together." or "The results should be posted by now." The word 'would' is more of an expression to say you probably will do something or you are in favor of an idea or such. It can be used as a question, request, or to express desire. For example: "I would love to teach you English!" or "Would you want to go see a movie with me?" or "That would be really cool, I'd love to go out for coffee on Friday!" I'm sorry, I understand that it is a confusing topic. I really did try my best! Let me know if you need any further explanation or help! (=