Basically for death certificates, you need to know where they died and it helps if you have a date of death or a date of birth to help them find it. If you only have a county, that's usually fine. Then you can order them from the state's vital records. Usually you can find that information online if you just do a search for, say, "Oregon death certificates." All the instructions for what to do and the forms you need to fill out should be fairly easy to find from a search like that.

If they're only a couple generations back, you'll need to list your relationship to the person, but I've never had anyone call to check or anything.

Hope that helps! It's pretty easy, really. :)