The way i started was going into a local gym and signing up. In my area, we have 2 main types of gyms. The first is the PAL(Police Athletic League). The second is the regular gyms. The difference is the dues. The PAL is a one time fee of $75 that covers the entire year. The NON-PAL gyms, you must pay monthly. Some I have paid as much as $150 a month and some as low as $12 a month. Depends on where you go. You will of course need to register and acquire a license. Which is $50 anually, for boxers at least. Not sure about MMA. We would only spar with them to help them with their boxing. All the license is, is insurance. In case something happens to you. It's essentially a license to allow you to participate in sanctioned matches. Otherwise it would be illegal for you to participate.
The license is a passbook that looks like a passport with a passport style photo and a sticker saying you are officially registered. Every year I needed to fill out paperwork from my gym, which by the way needs to also be registered. Unless your fighting unattached.
All you really need to do is go into your local gym, go in and say you want to start fighting. The trainers should take it from there. MMA in my area is more like $150 and upward a month. If you have any questions, feel free to ask. I fought for around 5 years. 2 broken ribs, a finger, a fractured jaw later lol Are you sure this is what you want to do? Asperger's will make it hard on you! Especially before the fights. You wait around for hours before state tourney's. After the matches there is a lot of talking. There are a ton of people while your training and sparring.
IF you live in the USA, if you give me the name of your town, I will gladly find you some gyms in your area.
HERE IS A PIC OF MY OLD LICENSE(PASSBOOK)
The license holds your fight record. Doctors have to sign off on it before and after every fight.