There are a couple of things that are important to know about tequila, one of which is absolutely crucial: the difference between "puros" and "mixtos."
What makes tequila different from, say, whiskey or vodka, is that it is made from the agave plant (actually, a particular species thereof). By Mexican law, to be labeled "tequila," at least 51% of the liquor must be distilled from agave; the other 49% can be distilled from corn, sugar cane, or whatever else is available. Agave is expensive, in comparison to corn or sugar cane, so such "mixtos" can be made on the cheap. Many of the most popular brands -- including the ubiquitous Jose Cuervo Gold that we've all gotten sick on at some time in our lives -- are mixtos. So, a bottle of this stuff contains about half real tequila, and half who-knows-what-else. If the what-else is distilled from sugar cane, for example, it is basically cheap rum; if it is distilled from corn, it is basically cheap corn whiskey. Do not drink this stuff under any circumstances. Would you order a drink at a bar made from half good tequila, and half the cheapest rum available? It's no wonder that people get sick and have terrible hangovers drinking mixtos.
In contrast, a "puro" is distilled entirely from agave: It is "pure" tequila. Look carefully at any bottle and search for the phrase "100% de agave": If it says that somewhere, it is a puro and worth trying. If it doesn't say that anywhere, it is surely a mixto, and you should take a pass. Note that the "100%" part is crucial. If it just says something like "made from blue weber agave," it's a mixto (i.e., it's made only partly from agave).