When you wish to downgrade to the iOS version that the SHSH is for, run TinyUmbrella, click the "Start TSS Server" button, and start iTunes. Hold the shift key and click on the restore button in iTunes, select the firmware file that you intend to install on your iDevice, and you're on your way.
TinyUmbrella, masquerading as Apple's TSS server, will tell iTunes that the firmware version that you are using is signed, allowing the downgrade to proceed. When it's all over, your iDevice will reboot, and you'll see the "connect to iTunes" screen on your iDevice. Click the "Kick device out of recovery" button on TinyUmbrella, your device will reboot, and your downgrade will be complete.