Bonds are issued by sureties and most sureties have claim forms on their websites. If not, a simple letter to the surety identifying the bond number, principal on the bond, and basis for your claim will suffice. If the surety needs additional information they will contact you.
Your question may be a little bit ambiguous. If you're referring to a "payment bond" or "performance bond" that you want issued to you, then Garret's above answer is correct. You'll need to apply for this with a surety.
However, you may instead be asking how to file a claim against a bond that is held by someone else. It is common for subcontractors or suppliers to file a claim against payment bonds held by general contractors on state, federal, or major private jobs.
To do this, you will need to prepare and send a "bond claim." This is basically a structured letter that is sent by certified mail to the general contractor. Here are some things that can help: