Upvote:4
It should just be a normal tourist visa process. http://www.ukba.homeoffice.gov.uk/visas-immigration/visiting/general/requirements/
You need to book an appointment with the UK embassy in the US (not sure which city you're in right now). If you're visiting your family, you need to get a letter from your family in London to invite you with their details such as passport and means of support.