Although a passport is not required, it is strongly advised that you have one. You are going to another country - a passport just makes sense.

A passport application takes about 4-6 weeks for processing. You can get either a Passport Book or a Passport Card.

Passport Books are $110

Passport Cards (approximately driver's license size) are $55.

To obtain a passport you must have 2 pieces of acceptable ID, a 2x2 photo and a completed Form DS-11. You CANNOT get a passport online, but you can print out the form. Many post offices have passport windows where you can apply. 

Website for US Passport info:

http://travel.state.gov/content/passports/english/passports.html