Shipping a trailer can be as simple as having someone tow it to its destination. Be sure the towing vehicle is equipped with a compatible hitch with functioning electrical systems, and that it is powerful enough to handle the load.
Depending on the size of your trailer, you may also be able to send it in a freight shipment. If your trailer is new or particularly valuable, this may be worth the extra cost, which will certainly be higher than the cost of having it driven.
The freight shipment will be more expensive if you pack the trailer full of heavy goods. Depending on how much stuff is moving to the same place, you may wish to pack the trailer full, or remove all portable parts.