Hmmm Chicago Swiss,
I will do my good deed for the day.
The process you are about to go thru will be painful!!
I brought my car from Germany and what an ordeal!! But that is another story. Talk about the Swiss and their paperwork!! I had to get that dig in there!!
I can point you in the right direction and let you run with it. Have fun!!
You will need
1. The registration
2. Shipping paperwork which brought the car to europe
3. Proof of insurance
4. Residence/work permit
5. Drivers license
6. Abgas test which is done here
You will have to check with customs also for crossing the border.
I had purchased my car within 6 months of arriving so they wanted TAX!!
But if you have proof you had the car for the time past this than customs may only be a paperwork shuffle. IE formula 11.010 d and or 13.20 A
All of this will be needed BEFORE you can register.

I live in Canton Schwyz but put my car thru the Luzern customs office as I didnt want the hassle of dealing with lines at the border in Basel.
Here are some numbers. The customs gentlemen in Luzern spoke pretty good english.....unfortunately I dont remember his name. Call and ask.

Then you can call the Schwyz traffic office (verkehrsamt) as the assistance there was good and they also spoke english. I speak well German so there wasnt a problem for me but they do hear your other accent and some try their english then.

Zoll Luzern
Luzerner Str 88
6014 Littau

Phone: 041 259 0170
this is the central number ask to be connected to the Zoll buro (office)

Traffic office Schwyz
Schlagstrasse 82,
6430 Schwyz

Phone: 041 819 2145
This number you can ask questions or get the number to the canton you live in
or google it ____________ verkerhrsamt

Good luck and I hope it works for you. I only have to laugh as the Swiss wanted even more paperwork to prove my Audi was made in Gemany after the title and all else were in German!!!!
Dx