Decide up front your functional requirements for the trailer. Then find or build a trailer that meets your requirements. Then get a hitch. Some trailers use classic 1.5" (or whatever it is) ball hitches, others are essentially proprietary, like the Bushtec. The best commonly available cargo trailers are the Bushtecs, but they may not meet your needs.
When pulling a trailer, be aware of your increased length. Few things will spoil your day as much as putting your trailer into somebody's front fender when merging in heavy traffic. In all likelihood, things will rapidly (very rapidly) deteriorate from there. The trailer will also "off track" a wee bit, which combined with its wider track means you gotta be careful when cornering not to allow the trailer to cut the corner and get into some sort of "situation."
When loading the trailer, pay attention to the load distribution, you want your tongue weight to be appropriate. Some of the squirreliness you see is due to improper tongue weighting. Also, make sure you do hook up the lighting harness. If you don't, you'll be replacing your connectors. DAMHIKT.
Parking with the trailer. Park so you can pull forward. Whether this means pulling through into a parking space, or backing into one, you always want to be able to pull forward if possible. Absolutely worst case scenario is when you have to back it uphill. The ST is already a porker, stick 100-350lbs of trailer behind it and its very difficult to back uphill. Thems is the times when you ask yourself "why didn't I get a Goldwing?"
Having a trailer is incredibly convenient. You can ride someplace two-up in the spring or fall when its cool, and have all your riding gear stowed as quick as you toss it into the trailer. Jacket, boots, pants, helmet, a trailer swallows it easily without fuss.