There are some folks on here who could give you a more detailed accounting but here's a basic rundown;
You must have collecting permits from the country where you propose to do your collecting. Some issue blanket permits others require you specify each species you plan to collect, some fall in between.
You must have export permits from aforementioned country. Most have export quotas on all the popular animals. If all the big exporters have already used up the quota on something you want, you may collect the animals but you're not getting them out.
You must have import permits from the U.S.
All of these cost money and take time, especially if you are applying for all these permits by yourself for the first time. Allow yourself at least 6 months to get everything lined up.
You can bypass the need for import & export permits by paying someone who already has them to do it for you. You get the permits to collect then take the animals to the import/export company you're using and pay them to bring the animals across borders. This is not cheap.
Another important thing. Not all airports have Customs facilities to allow them to receive shipments of animals/goods from abroad. There's usually about one airport per state that does. Find out what your closest one is BEFOREHAND. If you live out in the middle of nowhere in the midwest you could be looking at a full day of driving just to pick your animals up from the airport.
This is a basic outline, hopefully it gives you a rough idea of what you're looking at if you choose to go forward. It's a pain in the butt and requires a not inconsiderable outlay of time and money, that's why not many people do it. If you decide to go ahead do yourself a favor and find someone who has already gone through it to guide you along, and assume it's going to cost you 10-20 times what you expect. Have fun!