zhuzhits,
The process for buying from a private owner is the same for as process for buying from a retailer.
1. You must have proof that you've taken a state-approved handgun safety class.
2. Take this proof, along with detailed information about the firearm (make, model, serial #, caliber, barrel length) and detailed information about the seller (name, address, phone, employer) down to the main HPD office for your county. If this is your first time doing so, you'll get fingerprinted and be charged for a background check. I think the going rate is $18.25, cash, exact change.
3. Fill out lots of forms. Be sure that you know the contact information for both your employer and your medical care provider.
4. Wait two weeks
5. Return to HPD and pick up your Permit to Acquire.
6. Take that permit to your friend and trade it for his gun.
7. Take the gun back to HPD and register it.
8. Enjoy!
Note that steps 5,6 & 7 can be accomplished in one visit to HPD if your friend meets you there with his gun.