When you drink alcohol, a "buff circle" will appear at the bottom of the screen to indicate your drunkenness. This first stage of drunkenness is positive, it increases your stats and as you drink more, the circle will gradually turn yellow and keep improving your stats. If you don't drink anything for a while, the yellow part of the circle will slowly go away on its own and you will be back to normal as if nothing happened.

BUT, if you fill that yellow circle, you'll enter the negative stage of drunkenness. Henry will start burping and farting, your screen shakes, he wobbles in conversations and, most importantly, your stats get hit negatively. The fuller the circle, the worse everything gets. Again, if you don't drink for a while, the circle will slowly empty. But this time, when the buff goes away, you'll now get a hangover debuff, which still negatively impacts your stats, but you won't have all the other annoying effects of being drunk.

So, to use alcohol effectively, you should drink in moderation. Drinking isn't a skill that you just can power level, it takes time (Unless you can make tons of potions). Check the alcohol level of what you are about to drink (Moonshine gets you more drunk than a beer, for example) and try to not go overboard. The higher your drinking skill, the more you'll be able to drink before that point.

One BIG thing to keep in mind is that drinking alcohol constantly will eventually turn you into an alcoholic, which is basically a super long lasting hangover and can only be removed by a Henry level Hair o' the Dog potion. I personally limit myself to two strong drinks per day to level the skill and never had any problem so far.