This would be done by the current titleholder executing a deed in favor of him/her self and the other partner as either tenants in common or joint tenants with rights of survivorship. These are the two forms of joint ownership available to unmarried persons. The legal effect of a tenancy in common is that each of the owners owns a half interest. If one owner dies, that person's half interest passes to that person's heirs or the beneficiaries named in his/her will. The legal effect of a joint tenancy with rights of survivorship is that if one of the owners dies, the decedent's share automatically passes to the surviving owner.
You should contact a local real estate attorney to prepare the deed - it would probably be inexpensive. While it seems like a simple document and people often try to do them themselves or with the assistance of commercial legal forms and computer programs, it is very easy to do it inccorectly, and if incorrect, it is possible for it to be null and void, and therefore not to accomplish the objective for which it was intended.