Step One: Unzip and run redsn0w.
Step Two: Go to Extras and choose Custom IPSW.
Step Three: Select the firmware that fits your device and click open.
Step Four: Click Yes or No when it asks you about iPhone 3GS bootrom version (follow the onscreen instructions if you're not sure about it).
Step Five: Wait until redsn0w creates the custom firmware. It will place the file into the same folder where the original IPSW is.
Step Six: Enter Pwned DFU mode to prepare the device for iTunes restore. Follow onscreen instructions or this tutorial to send your device into DFU.
Step Seven: Go to iTunes and restore your device with the newly created custom IPSW file. Hold Shift+Restore and choose the firmware that begins with NO_BB, that's the IPSW with no baseband upgrade.
Step Eight: Wait for iTunes to upload the firmware and restore it on your device.
Done! Your device is now updated to iOS 5.1.1 without baseband update. That means that you are now on the latest firmware and your baseband is still unlockable.
You've installed custom firmware to your device which means that it should be activated right away. It it's not - use original SIM to activate your iPhone/iPad/iPod Touch. But if you don't have such card you can do several things here. Use redsn0w (manual here) or sn0wbreeze (manual) for iDevice's activation.
You should know that by now there are only tethered version of jailbreaks for iOS 5.1/5.1.1. We have to wait for about two weeks until untethered jailbreaks appear. So right now you have to use iBooty to perform tethered boot.
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