
How do I apostille
my US passport?

You can’t apostille your passport per se.
You can receive an apostille or authentication certificate once you make a copy of your passport then you get it properly notarized.
This depends on a few factors.
First, what country do you need to submit an apostille or authentication on your U.S passport copy to?
If the country is part of The Hague Convention you will receive a state-level apostille certificate from the secretary of state of where the notary you used to notarize your photocopy is licensed in.
If the country is not part of The Hague Convention you will receive a state-level authentication certificate from the state where the notary you used to notarize your photocopy is licensed in.
Then you will take your state authentication certificate and file it at the U.S Department of State in Washington D.C. to receive a federal-level authentication certificate. Then once you receive the federal authentication certificate on your passport copy you can file it with the U.S foreign embassy or a consulate office of the country of origin where your documents are being sent to.