"So, I have recently looked at joining the Army, still a little confused though. So, is taking the ASVAB test necessary, or can you just choose your MOS?"
Yes, taking the ASVAB is necessary so you can find out which MOSs you are qualified for. After you take the test, you will find out which MOSs you are qualified for. Then the recruiters will help you find out which MOSs are available.
"Also, can you only do one AIT, or can you do more after the first if you decide you want to do something else?"
It's possible to do another, but it could take a while. If you decide you want to do something else, you generally have to wait until your term of service is up. Then you can find out which(if any) other MOSs you can try for. Actually, that's the "official" line, but you can theoretically put in a Personnel Request at any time you want, although some units will STRONGLY discourage or just flat disapprove any requests submitted outside their standards.
"Would I be able to go to AIT for Aviation Logistics and then after doing that for a while decide I want to go infantry? Don't tear me up :???:, haven't talked to a recruiter or anything, and just started researching recently."
They don't like spending a lot of money to teach somebody one job only to have them leave for another job. That said, when it's time to re-enlist you sometimes have the option of going to another school or MOS. Your choices will depend on the MOS you are in and which MOS you want to learn. Getting into the Infantry is pretty easy, since there are LOTS of slots available in the field.