Download the application from the government website (link posted below). You can fill it out online or fill it out by hand. Print in capital letters and use black ink if you decide to do it by hand. If you are unsure about any of the information requested, leave the area blank and the postmaster will help you. Do not sign the application. This must be done when applying.
Find out where the nearest post office is that handles passport applications on the official website. Call ahead and check for correct hours and make an appointment if necessary. You must apply in person for your first passport.
Take your original certified birth certificate with you. It must have the raised seal. This will be sent in with the application and returned separately in the mail.
Take proper identification with you. This is a valid driver's license, government id, or other documentation that is listed on the website.
Have your passport photo's taken. These can be taken at many sites such as WalGreen's or even done at the post office. Be aware that if done at the post office they will charge twice as much as most other sites.
You have to pay two fees when applying and will need two separate checks, money orders, or cash. Currently these fees are $75 (application fee) and $25 (execution fee).
Be aware that it usually takes 4 to 6 weeks to receive your passport unless you pay extra fees to have it expedited.