US citizens need a valid passport and a tourist visa to enter the US.
The tourist visa is a simple online form where you will be required to enter your passport details, address, date of birth and the reason for your visit.
They will then ask you a series of questions about your history e.g. any criminal convictions, bankruptcy etc
Usually the decision to grant your visa is given within a couple of days and this too is electronic.
Sometimes some applications have to be seen by a real person and then the visa can take a few more days to come through.
I would always allow 2 weeks to get your tourist visa. These days you don't get much paperwork but please keep your application number and proof of your visa being granted with you.