After an emergency landing, what procedures should the pilot follow?
There seem to be two parts to your question. First, what practical steps can I take on the ground immediately after landing? Second, which authorities must be notified?

For the first point, there are just too many scenarios to have a single answer but basically you should immediately check for injuries or damage to property and activate the emergency services if required. After that, secure the aircraft to prevent any further damage, call your insurance company and inform the aircraft owner and local property owner (as applicable). I'd also suggest giving your family a call rather than have them hear on TV news that you were "in a crash landing".

There are more dramatic possibilities, of course: if you ditched or landed in a remote area or in extreme weather then actual survival could be your highest priority. But that's a topic for another site.

For the second point, at least in the US it's possible that you don't have to notify anyone. If no one is hurt, nothing is damaged, and none of the incidents requiring immediate notification occurred (see 49 CFR 830.5 and the AIM 7-6-2) then there's no legal requirement to inform anyone. The authorities in this case would be the NTSB, not the FAA, by the way. There's a more detailed discussion of these requirements here.

An additional concern that I know nothing about is liability and other legal issues. Getting legal advice - e.g. from your insurance company or AOPA - would probably be a good idea whatever the circumstances.