"just a reinstall" of Mountain Lion keeps everything else in place.
All you need to do is restart to your Recovery System:
Restart, holding Command-R, until you see the grey apple with the spinning gear. Your Mac will boot to the recovery partition, with just a menu, with a few utilities. You can then reinstall Mountain Lion through your internet connection.
Here's more info about that:
http://support.apple.com/kb/HT4718
You CAN choose to erase the hard drive first - but a simple reinstall does not do that, and just reinstalls Mountain Lion as a fresh system, keeping all your own files, apps and settings intact.
It's ALWAYS a good plan to be sure you have a good backup, such as Time Machine, or Carbon Copy Cloner, etc. before you reinstall.
Even though the reinstall process is usually pretty solid - occasionally, things do go wrong - and there's no harm in knowing you have a backup, even if it's never needed.
Also, be sure to run your software update after the reinstall, as the system can be downgraded, missing the latest security updates, for example.