On the positive side, access to a carport is usually easy, which is a clear benefit when converting a carport into living space. A roof already exists. You probably have an electrical line easy to access. Utilities are also most often easy to access. In addition, it will be easy to provide ventilation and exterior egress. A point of access into the rest of the house will probably be available, as well.
On the negative side, the space you are considering is already in use to protect your vehicle(s). You must consider whether and how you will have the same benefits as a covered parking space.
You will often need to construct a sub-floor to make the converted carport level with the rest of the home or construct more appropriate stairs for indoor use. You will need to connect heat/air, electricity, and possibly plumbing for your new living space. You will also need to insulate the ceiling and build and insulate the exterior wall(s). Finally, you must determine how the change will affect the resale value of your home if a result of the conversion is that the home has no covered/enclosed parking.