You can buy the mooring equipment as a simple cash sale. But an in place mooring implies some marine rights also and those are usually conferred by the local town.
Each town is different. Some require the current "owner" to give up his rights and then the town resells those to whoever is at the top of their waiting list, usually for an established price. Others let the current "owner" sell it for whatever he can get on the open market and then re-register it with the town. In Newport Beach, Ca moorings go for many thousands of dollars.
Other places like Maine I understand is a totally free market. Anyone can drop a mooring almost anywhere and can sell it for whatever they can get.
I would check with your local town, specifically the harbor master if there is one.