Some pretty sound advice here already. Let me throw in a few more things for thought...
If your vehicle doesn't already have a hitch installed, one can be added but it should be done by a reputable place. The reason hitches are mostly on trucks and SUVs is greatly attributable to the words "Body on Frame". Most trucks and SUVs still have these. Most passenger cars are built on a unibody platform now. These can still support a hitch, but it needs to be installed right.
You'll also need to splice in (it should be included with the installation) for wiring for the harness to the trailer.
Also, the vehicle will handle differently. If the rear springs/shocks/struts are getting dicey, replacing those will help vehicle stability tremendously.
Even on a smaller vehicle, if it isn't an excessively large or heavy trailer, there probably won't be a need for additional transmission coolers.
Lastly, while a dealership may be able to offer some advice you probably won't get much from the actual manufacturer other than "We don't recommend making any modifications to the vehicle...". The lawyers make us say that.
It really sounds more complicated than it is. If it's installed properly and you follow a few safety rules, it's no trouble.