First check that your Mac Mini can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
Whilst Apple have withdrawn Snow Leopard from their stores, you can still get it from Apple by calling 1-800-MY-APPLE (if you are in the USA) and they will supply the SL DVD for $20 for a single user, or $30 for a family pack that covers up to 5 Macs. You can also purchase the code to use to download Lion from the same number.
If you are outside the US call your national Apple Helpline:
If you're in the UK, use this number: 0871 508 4400
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.