It is not illegal to use private carriers like UPS or DHL in the states, but some do have a policy of shipping alcohol only when a contract was established a head of time and usually in a commercial relashionship. The best way I've found is to use a private carrier and clearly label the box as fragile, just as kmcogarable shows in the video.
If you happen to live in Austraila, then it's perfectly fine to ship beer across state borders!