If you get this error: "Something seems to have gone wrong...trying to recover. Recovery completed. If you want to retry jailbreaking, unplug your device and plug it back in", or similar.
Then,
1. Restore iDevice using iTunes - Go to iTunes, click on iDevice on the left then restore (or shift restore and select 5.1.1 firmware, if you have already downloaded firmware).
2. After restore is complete, click on the iDevice on the left and make sure it connects to iTunes store.
3. Load up Absinthe and click jailbreak.