I know very little on this subject, but it is very important if you are either playing out of the country, or booking someone from out of the country. I will basically just talk about what I have seen or heard from others on this. I don't really know the legal process for obtaining your work visa, but I do know that it can be very difficult and very expensive. Take what I say into consideration, but educating yourself, and learning the facts is crucial.
There have been countless last minute cancellations because a DJ was turned away by customs. This can devastate a party and people are not sympathetic to your situation. It can ruin you. I'm not 100% sure, but I think you could also get penalized and be banned from the country you were trying to get into for a couple years. If an artist gets turned away, they have to get right back on a plane and go all the way back home. This can be miserable for someone if they are on a 10 hour flight. You also may lose your deposit on the DJ, the airfare you paid, and may not be able to cancel the hotel. Also, anyone that bought a pre-sale ticket will want a refund, and many people will not show up to your event if they really wanted to see the out of town DJ. You may lose your venue rental fee and can blacklist yourself from ever throwing a show again. All this, and it wasn't even your fault. It was the DJ or their agency trying to pull a fast one on the government.
I've noticed the best way to fool the feds is to make your trip seem like you are just visiting friends to not raise suspicion. You should also stay in each city for a couple of days.
Packing very little music gear is essential. By little, I mean as little as humanly possible. A serato box, needles, and control vinyl are completely out of the question. Some people are too afraid to even bring DJ style headphones, CDs or in rare cases, a laptop, since it may be opened and looked through. They may need to borrow your headphones, so always have an extra pair handy. Many DJs now require promoters to have CDJ2000's so all they need to bring is a tiny thumb drive full of music.
You absolutely must convince the feds that you are on vacation. You need to have your story straight and say you are staying with friends (who are basically the promoter who hired you). You need to know their full names, address, and what you plan on doing during your trip. You can not have your actual name associated with your stage name either. If they google your name, and the first thing that comes up is a picture of you spinning in frond of a huge crowd, you are fucked.
When your tour is over, make sure any cash you made is safely in the bank. Nothing raises suspicion like a fat ass wad of cash after visiting 10 major cities. As I clearly stated before, this is just what I have either experienced, or heard from others, and I may be wrong about certain things. If this is a subject that is relevant to your situation, learn the facts.