At a basic level you don't need to do anything. A mouse is generically supported by Windows and requires no software to work. If the previous mouse had software provided with it you didn't actually need it but use Control Panel > Programs and Features to remove any software associated with it.
As it is a Microsoft mouse Windows will recognise it and needs nothing installed. However Windows Update will offer to install the Microsoft Keyboard and Mouse Centre application automatically. As I have said it is not really required but can add extra features that some find useful.