I installed a Class I trailer hitch on a small sedan. I ordered the hitch online. All parts fit perfectly. The supplied instruction sheet was excellent. No body mods were necessary. The job was surprisingly simple. It took me about 2.5 hours total. If you have safety glasses, a torque wrench, and assorted tools, I'd encourage you to try it.
Warning: Never exceed the towing capacity ratings of your car.
Step 1: Parts and Tools
Buy the hitch to fit your car. Several manufacturers offer hitches for most makes and models of car. (I ordered a Reese hitch from autozone.com for my 1996 Honda Civic sedan with 150K miles (don't laugh)).
Unpack the package. Look at the bag of parts. Read the instructions. Note the torque specs.
Gather your tools. Safety glasses (to protect your eyes), torque wrench (to make sure the hitch stays attached), hammer and chisel (to remove any schmutz on your car frame), inspection mirror (to make sure the carriage bolts are installed right), etc.
One change: To attach the ends of the hitch to the frame, I used big round washers instead of the u-shaped washers which came with the package. I'm not a mechanical engineer, but my gut didn't like the u-shaped ones. Caveat emptor: deviate from the manufacturer's recommendations at your own risk.
Step 2: Tips
1) The ends of the hitch attach to the car frame with carriage bolts and blocks of steel with square holes. Be sure the square part of the carriage bolt is fully inserted into the square hole, when it is installed in the frame. Otherwise it could come loose. I used a little round inspection mirror to look inside the frame. I did this several times while installing it and after it was finished.
2) The holes in my frame had a little raised flange around the opening. Ensure the big washers seat snugly against the flat surface of the frame. Do not get them hung up on this flange, else it will be weak and could come loose.
3) One of my frames was covered with shmutz (undercoating, road kill, whatever). Chisel off this crud to get a nice flat surface. Coat it with primer paint to prevent rust.
4) The center of the hitch attaches to the tie-down bracket under the trunk/boot with a small u-bolt. Remember to insert this u-bolt while you are test-fitting the two main frame bolts. Otherwise it is impossible to wiggle into place.
Step 3: Assemble and Finish
The rest of the job involves wrestling the hitch into position, getting everything to fit loosely, then tightening to torque spec.
One last time, ensure the carriage bolt heads are properly seated, and ensure the big washers are not hung-up on the frame hole's raised flanges.
Here are some more photos.