Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
should, would (auxs.)
In most uses, should and would are interchangeable, with the following exceptions. In the first person, should sometimes occurs meaning it could happen in the future, especially when the speaker may be trying for a bit of elegance (normally, its I would like to be there, but sometimes, even from the same speaker, youll hear I should like to be there). In other than first person, would is almost universally the American preference for describing something that may happen in the future. Should is used regularly in conditionals, as in If he should ask for me, tell him , and as the equivalent of ought to, as in She really should write her mother tonight.
Like shall and will, should and would have never really been used the way the rules have said Standard English uses them. Today Americans use would much more often than should, just as we use will more often than shall. If you are a native user of the language, you can safely choose whichever form feels right. In all but a few instances, the meanings will guide you.