It depends on the type of alcohol you seek.It can either be rather easy or very hard to find a gluten-free drink.
The easiest way to avoid gluten is to drink a fermented drink based on a non-grain such as fruit juice--wine or hard cider are definitely safe.
Though there is a division of opinion, the general consensus is that most hard liquor is safe. This is because, although many drinks (such as whiskeys) have grain alcohol has a base, gluten generally doesn't get passed through distillation. This also means neutral spirit is generally safe (as is vodka), and drinks based off them (like gin, liqueurs, and absinthe) will be safe as well. There are also hard liquors based on non-grains (like rum, tequila, and brandy) that will be definitely safe to drink.
Beer will be the toughest drink to avoid gluten. This is because of the general preference among brewers for barley (which does contain gluten). There are also a number of wheat-based beers which would not be safe. Perhaps the only known beers safe to drink would be African-based beers based of either sorghum or millet. But a couple warnings. Not only are these grains hard to obtain and to brew, but their end result is of a very different consistency from your average beer.