There are really three different verbs.
1    should
This verb (/ should/you should/he should etc) is used to talk about obligation, and in some other ways.

2    would
This verb (/ would/you would/he would etc) can be used to talk about past habits, and to make polite requests.

3    should/would
This verb — the conditional auxiliary — has the following forms:/ should/would you would he/she/it would we should/would they would

The conditional is used in sentences with if, and in some other ways.