Welcome to TID Joshua.
There are a few things that you need to know before starting a mobile detailing business.
First:
Are you doing this all legitimately, or on the side? If you are doing this as a main business, you need to incorporate, and get insurance. If you do any damage to a customer's car, you need to be covered. Also, set up a web site, with pictures of some of the work you have done. Another important thing to have is a vehicle that you can fit all of your equipment and supplies into.
As far as equipment goes, you need;
Either a shop vac or something like a metro vac
Electric leaf blower for drying the car after a wash.
A steamer (this is a nice thing to have but not necessary)
Electric Pressure Washer (also, not necessary, but nice to have)
Machine Polisher (either Rotary or DA)
A lot of polishing pads in each color
All types of MF towels for each task (you will need a lot of them)
Wheel brushes
Tire brushes
Long handle brushes for getting the wheel wells
small brushes for door jambs, and small spaces
At least 2 5 gallon buckets with Grit Guards
wash media
Chemicals:
Compound
Polish
Finishing Polish
All In One Polish
Metal Polish
All Purpose Cleaner
Glass Cleaner
Leather Cleaner and conditioner
Tire Dressing
Paint Sealant and or Wax
Car Wash
No Rinse wash
I am sure there are some things that I missed, and hopefully others will chime in.
Good luck and welcome to our little family.