It's as easy as installing the new version, preferrably to a different location than the old installation.
How do I update to a new version of Sonic 3 A.I.R.? (Windows) Now you can start the Sonic3AIR.exe there. on your desktop, or your documents folder, etc.).
Just download one of the ZIP files for either the stable or preview versions, and extract it to some location on your hard drive (e.g. How do I install Sonic 3 A.I.R.? (Windows)