I recently transferred from one university to another. Here's what I did.

(Before acceptance to new school, but after I sent my application in.)

1) contacted my current advisor through e-mail and asked what loose ends needed to be tied up, if any.

2) contacted the head of my major department at the new university and asked about credit transfers. (I'm a sophomore art transfer & some courses didn't directly transfer right off the bat, so I had to have a portfolio review to be able to transfer credit. This may be different for you, of course, but if you have any doubts they're always willing to help.)

(After acceptance to new school.)

3) contacted the transfer advisor at the new university and asked for a general sweep of what I needed to get taken care of

4) completed my FAFSA and submitted it to the new university (/ edit to add your new university)

5) checked my student account online for any initial issues with financial aid, holds, etc. took care of holds which included paperwork for financial aid or registrar

6) had an advising appt with my transfer advisor in-person (sometimes they will do this over FaceTime or phone call if you're far away) and got my schedule figured out

It was a fairly easy process for me. I would definitely get in contact with the new university ASAP and just ask admissions general questions, or find a department directory online and speak to an advisor in your specific department if you have questions about the program. If you can, I would physically go to the new campus and check things out. Talk with admissions/advising/financial aid/registrar in person. Check out the facilities and take a tour early-on so it seems less scary. They're happy to have you, so just shoot them an e-mail or phone call detailing how pure transferring and need the first step! :)

Hopefully I was at least a little help! Good luck!!