The second amendment in the Bill of Rights guarantees the citizens of the United States the right to bear arms. While it is illegal for that right to be stripped away by the government, it can be modified. As a result, if you want to carry a firearm on your person then you need to have a permit issued by your local government. Getting one of these permits isn't hard, but the qualifications may vary from one place to another depending on state and local laws.
Things You Will Need
Clean Criminal Record (felony convictions are barred from gun ownership, much less carry priviledge)
Go to your local police station. If you live in a city, go to the station that covers your address. If you live outside of any city limits then you will need to go to the county police in order to get your permit.
Fill out the necessary request forms for a permit to carry a concealed weapon. You'll need to provide all of your personal information including your address, name, social security number and others. The purpose of all of this is for the government background check that's done so you can get your carry permit. Some states, specifically those that require you to have a permit just to own a firearm, will require that you show proof of this ownership as well.
Have your fingerprints taken. In order to get a permit to carry a concealed weapon you need to get fingerprinted. You'll also need to pay a fee, which will have to be in the form of a cashier's check or a bank check, depending on the local and state requirements. Some states, such as Indiana, offer you the option of buying a lifetime permit to carry, in addition to a 4 year option.
Turn in your paperwork. It will take several weeks to several months for your application to be reviewed and for your gun permit to be granted or denied.
Getting a carry permit isn't a hard thing to do, but it does require you to put up with bureaucracy and red tape. Even in the most gun friendly states, this won't be a quick process.
Tips & Warnings
If you're not sure that you have a clean record, you might want to run a background check on yourself before you apply. Also, make sure you're familiar with your state laws so that you're well informed before you fill out the paperwork for your gun permit.