I assume you are interested in public universities, which are the majority in Spanish higher education. I do not know the criteria you need to fulfil in order to enrol, but I assume that since you are American you could ask the Spanish embassy in Washington DC, i am sure they can provide you with the right info, in the end, it is one of their duties there. They may even have it on their website. Maybe check the websites of the universities you are interested in, they may have interesting info for youas well.
As for the prize of tuition, it is very cheap compared to American Universities. I do not remember exactly right now but the tuition for my first year of phd four years ago did not go over 600$ and in lower levels it may be a bit more expensive, but not too much. it gets more expensive if you take courses again, which most people have to do at one time or the other so they make good business
And yes, it is cheap but not that you have many services or resources. Spanish universities are very different from American ones.
I hope this helps!
Elia