How you run possession (or any forced action really, madness, mind control, etc) is heavily dependant on both the skill of your players (as roleplayers) and what they are comfortable with. For most groups I have played with, I will generally privately communicate with the player, and let them know the personality, goals, capabilities of the possessing entity and trust them to roleplay it. I also trust the other players to notice something is wrong with their friend and take steps a bit more elegant than killing the host.

In cases of non-total control, I prefer to incentivise going a long with what the entity wants with xp (either bonus awards or an xp freeze) or possibly special powers. Especially with demons I like to offer deals. One of the best patterns here is big, brief effects for small, permanent costs. Maybe you can buy a critical hit for a hit point. If they like that the cost might go up. Turning that 1 into a 20 against the boss might sound good, by the way that one cost you 5. What would you pay for one more spell slot, what about a wish? Maybe 30 minutes of your time? The goal is to give the character reason to keep the demon around. Ideally think things are under control.

The most advanced form is much like what is used in Wraith: the Oblivion, you assign the demon to another player, give them some rules about what they can offer and cost, and leave it to them to meddle. Wraith is a game all about sharing your reality with the darkest of urges. If you are really interested in diving deep into these kinds of concepts it is well worth a read, even if you never find a group to play it. Though I do warn you, even if you don’t regularly use safety tools, Wraith is about abusive psychological manipulation and the death-drive. It’s not in itself toxic, but should be handled with care.

I didn’t do a full demonic possession but did a cursed item of Lolth which was very fun. The way I did it was each crit forced them to roll a doom die that is it hit a 1 the die decreased. As the die decreased the power of the item increased. Moreover the downsides and secretly how difficult it was to remove increased. So it started with a 1d10 and went down down to 1d4. They quit at 1d8. At lower die they got powers that would cause a roll of a doom dice which they could use at will.

This allows the players to dig their own grave as they use it more. Also the corruption starts slow and then ramps up more until it’s a full fall. It was fun to give then agency.

I would give them a list of demonic powers some of which would give some corruption but they can use it as often as they like. Let them have agency as they corrupt themselves