How do I sign up for a passport? And what do I need to know about it? I'm told I have to go to AAA, but that's about all I know about it. Does it matter where I'm going?
The US State Department has a website with full details on the passport application process.
You can use it to research the requirements, start the application form online (you'll end up printing it at the end), and determine whether you are eligible to mail in your documents (available for certain renewals) or must visit a passport acceptance facility (required for first-time applicants and some renewals). If you need to visit a passport facility, this service is available at selected US Post Offices and other government offices. An appointment is required at many locations.
You can also use the page How to Apply for a Passport. Answer the questions and it will tell you what form to complete, what documents you need, what fees are required, the requirements for photos, and where to submit your application.
It is possible to take your own passport photos if you have the required equipment, or you can pay someone at many drug stores or copy shops (or Costco if you're a member) to do it for you. Some passport acceptance facilities also offer photos for an additional charge.
It does not matter where you are going (unless you need the passport in a hurry), and you shouldn't simply show up at an acceptance facility without completing the forms, having the required documents in hand, and making an appointment if required.
This is a broad answer to a very general question. If you have a specific question about part of the process, you should ask it as a new question.
Apply for one at the US Post Office Details Here