You can buy firearms even if you are not a US citizen or permanent resident. Here is how to do it in California, which probably also applies to other states.
1. Apply for a hunting license from your state. You might need to take a hunter education class to get a certificate.
http://www.dfg.ca.gov/licensing/hunting/hunting.html
2. Bring your hunting license, passport, I-94, driver license, proof of residence (lease, utility bills, etc) to a gun shop. If you buy a handgun, you need to take an exam to get a handgun safety certificate:
http://ag.ca.gov/firearms/hscinfo.php
3. Pay for your gun, wait for 10 days, and the gun is yours.
1. Apply for a hunting license from your state. You might need to take a hunter education class to get a certificate.
http://www.dfg.ca.gov/licensing/hunting/hunting.html
2. Bring your hunting license, passport, I-94, driver license, proof of residence (lease, utility bills, etc) to a gun shop. If you buy a handgun, you need to take an exam to get a handgun safety certificate:
http://ag.ca.gov/firearms/hscinfo.php
3. Pay for your gun, wait for 10 days, and the gun is yours.