There's already pretty good advice in this thread. Until recently I worked nights in one of, if not the drunkest, cities in the U.S (Didn't get fired haha swapped to days). I'd be willing to say that more than two thirds of our patients at night if not more than that were under the influence of something, may grossly intoxicated to the point where I've seen a few get intubated just to protect their airway.
The best thing you can do is be friendly. You have to be authoritative but let the cops, if they're involved be the mean ones. With that said, sometimes you have to put your foot down. My partner and I had it pretty dialed both started out friendly but if necessary I'd become the "bad cop" while my partner would remain the "good cop" unless things got way out of hand.
Their destination is going to depend on local laws and protocols. Whether that be jail/the drunk tank or the hospital. Intoxication is generally a LE problem, not healthcare but there are requirements for who can go to detox and who has to go to the ER. Those requirements included vitals, medical complaint outside of being too drunk, active vomiting, and ambulatory/non-ambulatory. There's also no reason you can't release the patient to a responsible party and save the jail and hospital space except in really severe cases. Sure they'd *probably* be ok sleeping it off in a bed, on a couch or on the bathroom floor but I'm not willing to take that risk with my livelihood and own mental health just to save the ER bed in questionable cases that LE wont take custody of.
The ones that are out and vomiting need to be in left lateral or sitting up, I prefer sitting. Bio bags make great bibs, tear a hole near the rim on one side and pop it over their head so you can just hold the other side of the rim up and way from their face if they start vomiting rather than holding a tiny emesis bag to their face. Plus most unconscious, vomiting drunks will fill up a liter emesis bag pretty quickly.
Rarely is a drunk going to be a load and go unless there's some sort of underlying medical problem, severe traumatic injury, or you're unable to protect their airway but proper positioning and suction in real bad cases goes a long way. One thing I will say is NPAs in drunk people can be a real bad idea unless they're tongue is occluding their airway (ie profound snoring respirations). In my experience if they aren't already vomiting NPAs do a great job of starting the process. As much as they say they don't stimulate the gag reflex it's not true since often they are sized incorrectly and everyone's anatomy is different. Take it from someone who's had an NG and an NPA for :censored::censored::censored::censored:s and giggles, the NPA made me gag more than the NG did.
If you have more questions feel free to PM me, like I said, I've dealt with a TON of intoxicated patients in my short career.