Drunken Fist is a unique style of combat where, according to Might Guy, "the more you drink, the drunker you get, and the stronger you become". It can not be learned, taught, nor refined through training and practice. Drunken Fist fighters are not simply drunk: they become human powerhouses who'll strike unpredictably with an explosive fury and without any second thoughts about their actions. Once drunk, the user will lose their ability to know friend from foe and attack whomever is in their vicinity. The user's ability to dodge enemy attacks is also seemingly enhanced.
The Drunken Fist is not a reliable option because the 'drunken frenzy' that alcohol induces does not hold for prolonged periods of time; Lee is easily awakened from Drunken Fist with a simple scratch from anything which draws blood, sobering him up almost immediately. If he has not overcome his adversary by that time, Lee may be left at their mercy, as shown in his fight against Kimimaro. Lee also seems to have no memory of what happened while he was drunk.
In the anime, Lee developed and mastered a variant called Seasickness Fist, where he makes use of the nausea caused by seasickness to overcome the fact he can't drink alcohol.
The Drunken Fist is based on the 8 Immortals Zui Quan style of Chinese martial arts. However, in the actual martial art, intoxication is not a factor; rather, the characteristic "drunken" movements are actually feints that are made to confuse the opponent for a period of time.
In the English versions of the manga and anime, the sake Lee drinks is referred to as either a "potion" or "elixir" to avoid references to alcohol (as Lee is underage).
Despite the change to "elixir", Lee would still have had alcohol in his drink, as elixir is a type of medicine made of 40-60% alcohol, usually vodka or grappa. Being a medicinal item would also explain why Tsunade would have some while in the hospital.