Spare tire replacement is rather easy, again, thanks to the intervention of the Department of Transportation and National Highway Traffic Safety Administration. When the car industry moved to the donut spare as a way to save money and weight, DOT and NHTSA mandated two things: 1. That the tires be replaceable and accessible and, 2. That they be driven no more than 50 miles. Actually, you cannot really drive very far on one of the donut spares, as the handling of the vehicle is very much compromised by its presence. So you have to get it off as quickly as possible. Since it carries such a high pressure, it is possible that it can quickly wear out anyway. Usually, a visit to your car dealer will produce a matching replacement spare quickly, and it is the easiest way to ensure there is a match between your car and the spare.
For more info, see How Often Should You Replace Tires