The word "should" is the simple past tense of "shall." It has the meaning of "ought" and indicates a duty or expectation. For example, when you say something that has upset another person, you should apologize. It also has the meaning of "must" as in, "You should see that movie, you will like it."
The word "would"is the simple past tense and also the past participle of "will." It is used to express the future in past tense sentences such as, "He said that he would do it." It is used to express repeated or habitual actions such as, "He would walk in the park early in the morning." It can be used to express a wish, such as, "I wish he would stop making that noise." I wish he would come home." It can be used to express uncertainty such as, "It would appear that the boy is hungry." It would seem that you are right." And it can be used to express an intention or inclination such as, "Doctors would have us not eat fat."