I have one in process at the moment (Oxfordshire). I hit a reported (marked with paint) pothole. This cracked the rear rim, and destroyed a brand new tyre. I don't know the result yet, but I made sure I first re-reported the pothole to see how long they took to fix it, then put a claim in. In my case there was a standard claim form on the council's website. You can also request info from the council under the freedom of information act to find out if they have checked the road often enough, made the repair on time etc, which you can use to prove negligence (it this was the case).
Basically follow the instructions here:
http://potholes.co.uk/