I don't know how to get a job (being American, and all) or where to even start. I know I need some type of visa to be able to work, but what kind of visa can I get?
Unless you want to marry a UK citizen, the only kind of visa you can get is a tourist visa, which specifically forbids any type of work, paid or unpaid. If an immigration officer even thinks that you are travelling to the UK to look for work they will put you on the next plane back.
To employ a non-EU citizen a British company has to prove that they cannot find anyone in the whole European Union to fill that job, and furthermore the job has to be on a government list of occupations where there is a shortage. Given that the UK is a world class nation in many fields, even a top-level brain surgeon is going to have a hard time.