Start by asking your mechanic to recommend someone to perform the car hitch installation. If that doesn't work, check with companies that specialize in towing, such as trailer or RV dealerships. Some provide in-house installation, while others may recommend a good installer.
Some large moving companies, such as U-Haul, also provide trailer hitch installation. Make sure you discuss your planned use with the installer, because there are many different types of hitches and you need to make sure you get one that is strong enough. Although you can buy hitches separately and bring one to the installer, some shops offer a better deal if you buy the hitch directly from them.
Car hitches are also typically fairly easy to install yourself, since most are designed to match up with holes in the car's frame so they do not require any drilling. However, cars with low clearances may be difficult to work on without a jack to lift the vehicle safely. You also need some basic mechanical skills and tools to make sure it is installed properly.
The most difficult part of do-it-yourself installation may be the wiring. Most states require even small trailers to have working lights and electric brakes, which need to be wired into the tow vehicle to work. Be sure to check your car's manual to make sure it can handle the amount of weight you plan to tow.