Hi Kris! There are several ways to use both auxiliaries, I listed the most important ones. If you have further questions, feel free to ask.
Usage of "would":
for an imagined situation:
It would be nice to go to Spain this summer.
for imagined situations in the past:
Thanks a lot. I don't know what I would have done without your help.
Usage of "should":
to give advice or an opinion:
You look really tired. I think you should go to sleep. (I think it would be good for you to go to sleep.)
to say we expect something to happen:
You have been studying hard for your exams, so you should pass easily.
to say that yomething didn't happen, but it would have been the right thing to do:
We had a great time yesterday, you should have come. (You didn't come, but I think it would have been good for you to come.)
I'm feeling really bad. I shouldn't have eaten so much for dinner. (I ate too much, as a result of which I feel bad, and now I think eating too much was a mistake.)
Hope this helps.