Cornell has a nice set of publications and lessons on soils and fertilization online. Here are a few, some more in depth than others, all readable:\
(URL broken, paste back together)
Not all state ag schools do soil testing for the general public now, alas, but this is Cornell's soil testing lab faq, typical of many.
If your state does not offer soil tests and you can't find a reasonable commercial lab, check with extension services in surrounding states to see if they'll do out of state testing. I know that Iowa State does or did do out of state testing, but the out of state tests waited for them to work through any backlog of in-state testing -- that's probably true of any state lab that does out of state samples. P,K and pH and lime requirements are a good basic starting spot for garden soil analysis. Most home gardeners really don't need much more than that except in unusual circumstances, in my experience.
Kay