My son is buying a vehicle and the person on the loan as a co-signer broke up with him. My son has made almost all of the payments. Now when the loan is paid off, how does my son get his ex's name off of the title?
This will probably require asking the SO to sign a quitclaim and/or to "sell" him her share of the vehicle's ownership and getting it re-titled in his own name alone, which is the question you actually asked.
To cancel the cosigner arrangement, he has to pay off the loan. If he can't or doesn't want to do that in cash, he'd have to qualify for a new loan to refinasnce in his name only, or get someone else (such as yourself) to co-sign. Alternatively, he might sell the car (or something else) to pay what he still owes on it.
As noted in other answers, this kind of mess is why you shouldn't get into either cosigning or joint ownership without a written agreement spelling out exactly what happens should one of the parties wish to end this arrangement. Doing business with friends is still doing business.