Assuming I have a grill and someone I know uses it, without my permission, to cook meat from a neveilah (or perhaps not, but kosher species without certification). What is the status of the grill and how difficult is it to kasher without specialised equipment?
The Shulchan Arukh rules (OC 451:4) that a vessels used on a fire like a skewer or grill need to be heated up until sparks come off of them in order to kasher them. My understanding is that this is about 1000 degrees Fahrenheit or when it glows red. If it is earthenware you'd have to refire it in a kiln (ibid. :1). I can't comment about the specifics of any case, so practically you should CYLOR about the setup and different parts of any particular grill.
Assuming that you're only talking about the grill proper, i.e. the metal grid the meat rests on, you would need to do libun. The required temperatures can be reached with a propane torch. YMMV as to whether or not a propane torch counts as special equipment.