When the vet did Lacey, the vet basically hung the halter she uses when floating teeth, from the rafters of Lacey's run in shed. That halter held Lacey's head up while she was sedated and there wasn't a need for any "apparatus".
Depending on your vet, they'll probably either hang a halter from a rafter beam (I've seen that before, not just with my vet), or have some other method.
When Lacey got her teeth done, the vet set up the halter, put Lacey in it, sedated her, put the mouth opener thingy in her mouth, cranked her mouth open, looked at her teeth, felt around, then started working on her teeth. The teeth took probably 45 minutes, going slowly because Lacey kept "waking up" and getting sassy, and because the vet was constantly checking her own work.
Then, after the teeth were done, I had to contain Lacey away from grass and hay for 2 hours to make sure she didn't eat anything (the sedation can hinder the swallow reflex).
After 2 hours, I let her out and made the mistake of feeding her grain, apparently the swallow reflex hadn't woken up yet because Lacey choked on her grain. Thankfully I was able to massage the blockage out without needing to call the vet back.
Anyway, that was my experience. :)
Fabio - 13 year old Arabian/Lipizzan gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.