Before you hit the road, make sure everything is connected & working properly.
First, check the hitch. For a regular ball hitch, the tongue on the trailer should be properly attached to the vehicle hitch, with the locking mechanism snapped and lock pin in place. If the hitch isn't secure, it could off and go through someone's windshield. A trailer connection to a vehicle should also have two chains, criss-crossing in an X shape, between the vehicle and the trailer.
Check the connection by pulling up on the trailer to try to pull it off the hitch, which you shouldn't be able to do. If you can pull the hitch off, it must be reattached. Also check the clearance of the connection, and make sure any wheel or stand for the trailer is in the up or drive position.
Next, check the brake lights and signals. Connect the electrical wires from the trailer to the vehicle. If no one is available to tell you whether the lights work when you apply the brakes, use the reflection of another vehicle, window, or other reflective surface; or check in the dark.
It is very important that the brake lights work on the trailer. Otherwise, motorists are unable to tell when you are slowing (and in the dark, they won't be able to see you at all).
Check tire pressure and take a close look at the tires for any signs of wear or cracking.
If the trailer and hitch connection is good, and the trailer signals are working, you're ready to drive.