Replacing only one tire might not be a good idea. If all four tires have 50% or more tread remaining, changing only one will result in one wheel spinning faster than the others, potentially sending erroneous signals to the traction control and antilock braking systems.
Replacing just one tire may be more trouble than it's worth, and you'll end up spending much more than if you bought two or four tires instead. Most of the manufacturers suggest that you replace all four tires at the same time.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.