In your cups
Or, how to describe a British person who is under the influence.
Most words that I can think of for a drunkard or drunkenness are shared in the UK and the US. A drunk is a drunk, but one curiosity that's often misunderstood—even here in its place of coining—is the term "tosspot," which refers to an habitual drinker (I believe it can be found in the works of Shakespeare, though I don't know which play). However, since the terms "toss" and "tosser" are vulgar terminology for the practice of self-abuse and one who indulges in such practice, tosspot has, by misunderstanding, come to mean the same as tosser in the modern vernacular ("wanker" is yet another English slang term for an onanist).
So far as the condition of drunkenness is concerned, London rhyming slang provides two popular terms:
The first is to be "Mozart (or Brahms) and Liszt," which is to be pissed, ie drunk (eg "she's slightly Mozart" or "he's completely Brahms").
The second is to be "Elephant's trunk," which is to be drunk (eg "he's a bit elephant's").
There are numerous other terms, and a selection follows. Some of them may be familiar or also used in the US. I tried to order them in groups to avoid an unrelieved list in a long, solid block of text.
So, then, an archaic term to start: In his/her/your/my cups.
With reference to alcoholic beverage:
Beered-up; bevvied (to go for a bevvy is to go for a beer, bevvy being an abbreviation of the word "beverage"); lagered (from the beverage lager); lagered-up.
Alluding to maritime references:
Groggy (from "grog," the Royal Navy's term for rum); three sheets to the wind; under full sail.
Alluding to a body or its function:
Arseholed (US equivalent would be assholed, I suppose); bladdered; legless; off his/her/your/my face; off his/her/your/my tits; pie-eyed; pissed; pissed up (but not pissed off, which is to be disgruntled, nor piss off, which is an instruction to an irritating person); shit-faced.
Alluding to medical practice or condition:
Transfused; medicated; anaesthetised; feeling no pain; comfortably numb; tired and emotional.
Alluding to specific creatures:
Drunk as a lord; drunk as a skunk; (pissed) as a newt (eg "I'm afraid Eric is 'as a newt' after all that beer"); rat-arsed; ratted.
Alluding to various processes:
Boiled; lubricated (also well-oiled); loaded; pickled; plastered; potted; soused; stewed; tanked-up (ie the tank, as a receptacle, is filled).
Alluding to destruction or punishment:
Annihilated; battered; half-cut; hammered; lashed; leathered (I suspect from the unenlightened historical disciplinary practice of some father's using their belts to chastise their offspring); mullered (possibly from the verb "to mull", ie to grind down, or from a Romany word-root associated with death or dying); smashed; slaughtered; wasted.
Alluding to loss of sensibility or equilibrium:
Blotto; blootered; goggled; sloshed; sozzled; squiffy; tipsy; woozy; top-heavy; can't stand up for falling down; can't lie down without holding on.
Two of my personal favourites: Trolleyd (where one is in such a collapsed state that one is only fit to be put in a trolley [shopping cart] and taken away), and wellied, (derived indirectly from wellington boots [heavy, waterproof, knee-length rubber boots]. The metaphorical phrase to "give it some welly" is to apply force to one's activity [such as kicking a football—though obviously one wouldn't literally wear wellingtons to do that], or to accelerate to high speed when driving a car. To be wellied suggests that one is in a state of having been "given some welly").
There's quite a mixture of traditional and modern expressions in that list.
Expressions describing celebration:
A "do" is a party or celebration (pronounced in the same way as in "don't do that"), which would be used in a phrase like "we're going to have a do to celebrate our son's engagement." A "bash" is something similar, as is a "knees-up," another term for a celebration, as in "we're having a bit of a knees-up." All of those are probably quite old-fashioned, but not as old-fashioned as the almost archaic "beano" (a celebration), which really only remains in public recognition as the title of a well-loved and very long-lived children's comic paper, The Beano, which is probably the last remaining place anyone would find the expression "slap-up," too. In the children's papers available during WWII (printed less often, with fewer pages and in a single colour to preserve resources in wartime), the protagonist of a particular feature would often conclude that episode's adventure with a feast: something much dreamed-of by hungry children subject to rationing. Such a bountiful celebration would often be described as a "slap-up feed" or "slap-up feast." This convention persisted for years afterward, and I remember the comics of my youth containing similar "happy endings". I suspect they may still. A phrase with similarly extravagant meaning is "blow-out," eg "a blow-out lunch."
More contemporary is the expression "on the lash," which is to be out for an unrestrained evening of alcoholic revelry.
Other associated rhyming slang:
Curiously, the common practice of truncating the full rhyming expression (eg "titfer" being the abbreviation used for "tit-for-tat," rhyming slang for hat) doesn't hold for many of these examples.
Rub-a-dub: pub, eg "pull your daisies (daisy roots = boots) on, we're going to the rub-a-dub."
Battle cruiser: boozer (a popular expression for a public house), eg "get your billy (billy goat = coat), we're going to the battle cruiser"
Gregory Peck (or bushel and peck): neck, eg when offering a drink to a friend: "get that pint down your Gregory (or bushel)."
Kitchen sink: drink
Baby Giraffe: half (a pint [of beer])
Fine and dandy: brandy
Finger and thumb: rum
Gold watch: scotch (although "gold watches" is also a slang term with something to do with expectoration)
Vera Lynn (the recently deceased British singer famous for morale-boosting songs during WWII): gin (another—non-rhyming—slang term for gin is "mothers' ruin")
Pig's ear: beer (another—non-rhyming—slang term for beer is "suds," from the foam atop the drink. "Sudsing up" is drinking beer)
Laugh and titter: bitter (a British style of beer)
Forsyte Saga: lager (after the novel by John Galsworthy and—more especially—its later adaption as a TV series in the 1960s). In use: "give us a Forsyte, I'm parched."
A few more expressions:
I imagine "being the worse for wear" is not unheard of in the US as a euphemism for being drunk? I'll add it, just in case.
One of my father's expressions, when referring to someone who might have overindulged, was "he's had more than a sniff of the barmaid's apron."
Another term, of military origin, is "one over the eight" which is one drink too many—presupposing that eight glasses (presumably pints) somehow remains on the right side of the line.
The deplorable habit of drinking lager gained popularity over traditional British brews in the 1970s and 1980s. The habit was chiefly with the younger end of the market and gave rise to the terms "lager lout" and "lager frenzy", both self-explanatory.
I was surprised to discover that "beer goggles" is of American coinage, so you'll already familiar with this term for drunkenness making a member of the opposite sex appear to be more attractive than they otherwise might.
A common saying in the UK, which references drinking culture but is a metaphor for incompetence, is "he/she couldn't organise a piss-up (a serious drinking session) in a brewery." My Dad used a more polite equivalent: "he/she couldn't arrange a bun-fight in a bakery," which also benefits from alliteration. A bun-fight is another term for a celebration but clearly implies the presence of baked comestibles rather than alcohol.
In the UK, taking turns to buy drinks for the immediate assembled company (buying a round) is good practice. The declaration "It's my shout" is a statement of intent to buy a round. An exuberant encouragement to a member of the company to buy a round might be "Hey! [Name]! Get 'em in!" Someone who is well known for habitually not standing their round is said to have "short arms and deep pockets."
Having Australian friends, I have also heard the following antipodean expressions:
Bottle-o: the equivalent of the off-license, beer-off or liquor store;
Sink a slab: to drain a 14-pack of beer;
A cold one: beer;
Frothy: beer;
Stubby: bottle of beer;
Tinny: can of beer; and
Skull: to drink ("Here, mate, skull that!" The English equivalent might be "get that down your neck!" or "get your laughing gear 'round that!")
You are now prepared for a night on the lash.
Also see Four legs and at least two grapes.