You will need to go by a US Customs office and fill out a Customs Form 4457 before you go on your trip.  The US Customs Service has offices at any large international airport.  Check your government pages in the phone book to find the phone number for your local Customs office. 

DO NOT WAIT UNTIL THE DAY OF YOUR DEPARTURE TO GET THIS FORM AT THE AIRPORT. 

GET IT AHEAD OF TIME!

Here is the link to download the US Customs Form 4457 - http://www.cbp.gov/linkhandler/cgov/toolbox/forms/4457.ctt/cbp_4457.pdf

Your gun should be packed in a crash resistant plastic or metal case that locks.  Don’t use the plastic case that’s on sale at the end of hunting season for $19.95.  In the US, you will need to make sure you get to the airport early enough to have your gun inspected by TSA before it is placed on the airplane. 

Call your airline about details of packing guns and bullets.  They are the final word.

Here is the link for the SAPS form 520 (Import Permit) - http://www.saps.gov.za/crime_prevention/firearms/forms/english/e520.pdf

Here is the link for the SAPS Form 520 instructions - http://www.saps.gov.za/crime_prevention/firearms/forms/english/ei520.pdf

Here is a link for hassle free firearms import permits - http://www.riflepermits.com/