Tipsy

Every wine, beer and cider gives you its buff and one level of Tipsy. It’s fun at first: a sway, hiccups, and a little liquid courage. Keep going and it starts to cost you: dark edges, heavy eyes, queasy spells, weak arms, then heavy legs and stumbling. It tops out at level 5.

Levels

Through your eyes: sober

1The view sways gently, the edges of the screen darken a little, liquid courage: 5% knockback resistance and 10% less fall damage
2The sway grows, the dark edges close in, liquid courage: 10% knockback resistance and 15% less fall damage
3A stronger sway, and hiccups: a harmless little hop, with a sound, heavy eyes: now and then they fall shut, liquid courage: 15% knockback resistance and 20% less fall damage, and now and then a spell of Nausea (15 s)
4Everything above, and a heavier sway, long blinks: sometimes your eyes stay shut a while, slurred chat: stretched letters and the odd *hic*, Nausea comes much more often, you're too drunk to enjoy it: drinks give no buff any more, the courage is gone, rowdy: now and then you throw a punch at whoever is in front of you, and villagers won't trade with you, andWeakness
5Everything above, and the world really spins, you feel sick more often than not, you stumble sideways now and then while you walk, andWeaknessSlowness IIMining Fatigue II

Other players see you sway a little and see your hiccups too. Hover over the Tipsy effect in your inventory to see what your current level does.

One drink too many

Already at level 5 and still drinking? You black out. Your eyes fall shut and you keel over, stars circling your head for everyone to see, and for a few seconds nothing can hurt you. Then you wake up. Where? That depends on the night, and there are more ways to wake up than you’d think…

You’ll be hungry and shaky for a while, back at Tipsy I, and your pockets may hold something you don’t remember picking up. Nothing you had is ever lost.

Rowdy

From Tipsy IV, you get rowdy. Now and then your arm swings by itself and throws a real punch at whatever is right in front of you: half a heart of damage and a shove, whatever you’re holding. It never hits tamed pets, iron golems or armor stands, and it only hits other players where PvP is on. Villagers and passers-by are fair game, though, and they remember it.

You’re also cut off: villagers and wandering traders shake their heads and won’t trade with you until you’ve sobered up. Do your trading before the fourth drink.

Sobering up

Wait: each level wears off after 90 seconds, one level at a time. A new drink gives every level a fresh clock, so at Tipsy V you’re sober again after about 7.5 minutes without another drop.
Milk clears it completely, like any effect. It clears your drink buffs too.
A water bottle or any juice (Grape Juice, White Grape Juice, Sweet Berry Juice, Apple Juice) lowers it by one level right away. Their tooltip says so: Lowers Tipsy by 1. Only a plain water bottle works, no other potion.
Sleep it off: go to bed and sleep through the night. It has to be a night that’s really skipped: get up early, or lie awake while the others on the server stay up, and you wake up as tipsy as you went to bed.

Good to know

Sneak at Tipsy V and you never stumble. Swimming, riding and flying don’t stumble either.
Water gets you out of the bad levels fast, but the levels below keep their own time, so it doesn’t make you sober sooner overall.
Tipsy only looks after its own side effects: a Slowness or Nausea from a potion or a command is left alone.
Chat links, commands and @mentions are never slurred.
Other players see you sway, hear your hiccups and see your rowdy swings, but not your dark screen edges or your blinks.
Want the whole story of a blackout? Every place you can wake up, the odds and the souvenirs are on Blackouts. Spoilers, of course.

Settings

Server owners can switch Tipsy off entirely (the non-alcoholic mode) or turn off slurred chat, stumbling, blackouts and Rowdy one by one; every player can tone down the sway and the vision effects for themselves. All options and defaults are on Configuration.