If you are married to an American and apply for a visa to move to the US, you are issued a conditional residence permit if you've been married for less than two years. After two years you can apply to have the conditions removed. If you've been married more than two years, you are granted an unconditional residence permit. There are restrictions on the time permit holders may spend outside the US, though if you acquire US citizenship that becomes irrelevant.
There are different ways of going about it, but the easiest is if the American spouse has lived in the UK long enough to petition through the Embassy. This requires having a sponsor, or enough assets to fulfill the requirements of the affidavit of support, or an offer of employment in the US that will meet minimum salary requirements. The couple can stay together in the UK during the process. The alternative is to have the American spouse petition from the US, which means being separated for some time.
It's actually not as bad as it sounds, and no worse than the process to get here--just a bit more tedious.
