Welcome to the Apple Support Communities
Have you purchased OS X Lion? If so, check that it's not hidden in your Apple ID, so unhide it > http://support.apple.com/kb/HT4928?viewlocale=en_US&locale=en_US Finally, you will be able to reinstall Lion.
If you want to go back to Snow Leopard, your Mac should have come with DVDs or a USB drive. If your computer came with a USB drive, just insert the USB drive, hold the Option (Alt) key while your computer is starting, choose the USB drive and reinstall Snow Leopard. You may have to erase the hard drive before installing it.
If your Mac came with DVDs, you need an external optical drive or another PC or Mac to use Remote Install Mac OS X