What's a good way to taste a variety of alcoholic beverages?
As far as beer goes: Many brewpubs will offer a sampler (or flight) of beer that includes small (few oz) glasses of many of their beers from IPA to stouts and wheat beers. You get a few sips of each beer for the price of a pint (or so) and you can determine what you like or don't like. Also, sometimes brewpubs offer samples of their beers if you ask. I went to a place offering habanero beer, and definitely wanted  a sip before buying a pint. It's not always advertised but worth asking if you have an interested in something in particular.

For wine: Many places that sell wine also offer tastings on occasion, also wineries generally have tastings if there are any in your area. Wine stores usually will have a red and a white available during tastings and the person in charge of the tasting can recommend what kind of food to pair it with. Tastings are a great way to get to know what kind of  wine you like!

For liquors: Finding a local distillery can be tricky if there are none where you live, but I'm lucky to know of a few near me that have tastings for a small fee. A caveat, though, liquor can be hard to drink for some without being mixed with some sort of mixer (juice, soda, etc). So just keep that in mind, when you sip some gin, you may enjoy it mixed with tonic even though you dislike it on its own.