If you realize that you've misplaced your passport, or it was stolen within the United States, you'll need to appear in person at a passport agency or acceptance facility. In addition to a form and a fee, you'll need to present proof of U.S. citizenship, which could be an expired passport in your name or a certified birth certificate. You will also need to provide valid ID, like a driver's license.
If your passport is lost or stolen abroad, you'll need to go to the nearest American embassy, where officials will ask you to prove your identity in order to issue you a new passport. The most reliable method of proving your identity is to carry a copy of your passport with you on your travels. Make sure to keep the copy in a separate place from your actual passport to lessen the chances that they will be stolen at the same time.
You'll be even safer if you scan your passport and make a digital copy before you go abroad. Email the digital scan to yourself before you go, so that if necessary you can download and print it out at an Internet cafe. You can also keep a digital copy of your passport on a jump drive, but again, store it separately from your passport itself.
If you don't have a copy of your passport, officials will ask you for your passport number and date and place of issue, so it's a good idea to have those things memorized before you go. Friends or family at home may also fax copies of identifying documents such as birth certificates or driver's licenses, so it's a good idea to leave copies of those things with them. A travel companion may also vouch for your identity.
