I'll start by assuming you are heading to South Africa. Different countries have different regulations, of course.
The first thing you need is a customs declaration form (4457) from US customs. You can get this at most international airports or a local customs office. You need this to get your guns back home, and it serves as proof of ownership when in Africa. You can get your gun permit upon arrival in south africa, and it takes about an hour or two depending on the number of people on the same plane traveling with firearms. Another option is to pre-apply for the permit, and several companies offer this service for a fee. Gracy travel and Air 2000/Hunters support are the companies I am familiar with. A bit pricey, but speeds your arrival and nice to know things are set before you arrive.
At least get on their web sites and read their info. There are strange nuances to every country, but many ban any semi-auto rifles and handguns typically require more paperwork.
If you provide the specifics of your trip I can be more clear. If properly prepared, traveling with your firearms isn't a big deal.
Bill