"I should do my homework."
Translation:Jeg burde lave lektier.
Sure. :-) But in English for me, if you just say "I should do homework" it's less specifically about today's homework, and more about homework in general, or perhaps about some homework that's not due for a few days. (Usually. You can say it to mean today's homework, but it still feels a little detached.) And certainly a parent would always say "Do your homework!" over "Do homework!" -- except as a general exhortation.
Hm, let's try a different approach. I'm not sure if it works all the time, but it sounds good with the examples that I tried.
Skulle is used when there's a certain reason behind doing it, for instance because someone told you to do so: "Jeg skal lave lektier fordi min far sagde det." Or "Jeg skulle til byen" because you need to do something in the city.
Burde is used when you're doing something to achieve a certain goal. "Hvis jeg vil lære engelsk, burde jeg læse denne bog."
The difference is often small, though, and depends heavily on context. "Jeg skulle lave lektier" would be good as well if the context is that you really don't want but someone forced you to. If you do it because you don't want to get punished next lesson or want to improve your grade, you should use burde.