With Passports now required for travel to even Mexico and Canada* getting a passport before you need it is wise. If you have never had a Passport or yours is older than 15 years or you were 16 before receiving it follow these instructions.

You will need:
To apply in person
Form DS-11 completed
Proof of citizenship
Proof of identification
Money to pay for the processing

*If you are traveling by land or sea to Mexico, Canada, the Caribbean, or Bermuda you can use the Passport Card which applications are being accepted for beginning on February 1, 2008.

Step 1: Fill Out Form DS-11 and Find an Acceptance Facility

Go to the U.S. Department of State website and fill out form DS-11. Print out the form but do not sign it. Locate a Passport acceptance facility. You can find those nearby by using the Passport Acceptance Facility search page. Make an appointment if necessary, ask what forms of payment are accepted and see if they provide picture taking services or if you need to bring your own photos.

Step 2: Gather Your Documents and Money

Accepted proof of citizenship include:

Certified birth certificate ("A certified birth certificate has a registrar's raised, embossed, impressed or multicolored seal, registrar's signature, and the date the certificate was filed with the registrar's office, which must be within 1 year of your birth." Be certain that your birth certificate is certified and not just an unofficial copy.) IF you need a new certified birth certificate just go to the website of the state you were born in (usually their department of health and division of vital records) instead of going to a commercial service. I just compared a PA certificate: at the state site is $10 and at a commercial service is $32.
Certificate of Citizenship
Naturalization Certificate
Consular Report of Birth Abroad or Certification of Birth

If you don't have any of these you need a Letter of No Record issued by your state and as many of these as you can provide:

Census record
Baptismal certificate
Doctor's record of post-natal care
Hospital birth certificate
Early school record
Family bible record

Further options are available including an Affidavit of Birth (form DS-10) with more information available on this page.

You also will need a current and valid proof of ID:

Naturalization Certificate
Driver's license
Government ID: city, state or federal
Military ID: military and dependents

Photographs:

You may provide your own photograph or have one taken if you go to a Passport Acceptance Facility that will provide that service. A fee may be added for taking the photograph. Your photos must be:

2x2 inches in size
Identical
Taken within the past 6 months, showing current appearance
Color
Full face, front view with a plain white or off-white background
Between 1 inch and 1 3/8 inches from the bottom of the chin to the top of the head
Taken in normal street attire

(Uniforms should not be worn in photographs except religious attire that is worn daily. Do not wear a hat or headgear that obscures the hair or hairline. If you normally wear prescription glasses, a hearing device, wig or similar articles, they should be worn for your picture. Dark glasses or nonprescription glasses with tinted lenses are not acceptable unless you need them for medical reasons. A medical certificate may be required.)

Payment:

If 16 or older the fee is $97. Under 16 the total is $82. For faster delivery of your passport and proof of citizenship ID add an additional $60. You will want to verify with the Acceptance Facility which methods of payment they will accept.

Step 3: Check the Status of Your Application Online

The Department of State provides a site that lets you check the status of your applicationcheck the status of your application.

It currently can take up to 12 weeks for your Passport to be processed and sent to you.

This Instructable was written with extensive reference to the Department of State Passport Services Office website. I also just in February went through this process so had just gone through the hoops myself.