Contrary to popular belief, you need a visa to move to the UK if you are an American citizen. The only exception to this is that if you are visiting with no long-term plans, you can stay in the UK without a visa for six months – but you cannot work during your visa-free stay.
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Passport holders of these countries can visit the UK without a tourist visa
If you are a non-EEA national (including British) and wish to stay in Spain for longer than 90 days, you will need a visa. You should apply for the visa that suits your purpose from a Spanish Consulate in your home country.
Spain is a party to the Schengen Agreement. This means that U.S. citizens may enter Spain for up to 90 days for tourism or business without a visa. Your passport should be valid for at least three months beyond the period of stay.