First, you need to know what style of beer you are shooting for. In this respect its very much a historical excercise and the responsiblity lies on YOU, the beer drinker, to have an idea of what a specific style should have. In general a beer should never smell skunky or have an "off flavor". Off flavors can best be described as sour, tart, or anything along those lines. Unless you're drinking Belgian Lambic, you shouldn't encounter this flavor. If you do, that's a sign of contamination (read: bacteria or wild yeast) growing in the fermenters at a level that competes with the brewers yeast.
As a homebrewer this will be your greatest challenge. Off tastes are the hallmark trait of poor sanitation and/or low yeast pitching rates. The former is directly related to the methodical nature that you brew you're beer. The latter is really about not being lazy and growing up a yeast starter so you're little yeast buddies take off much much faster than anything else and crank out alcohol that stops anything else from growing.
Since a long discussion on styles is in the works as I continue beer 101 I'll save the specifics for later, but here are the characteristics you should look at when tasting beer. It's also not a bad idea to work through the characteristics in this order.
1)Color: Is the beer the correct color? If it's called a stout you shouldn't be able to see through it easily in the glass. Likewise, a pilsner should have a very light / pale color
2)Aroma: Does the beer have the appropriate aroma for the style? A true Weissbier should smell like bannanas, while an IPA should have a pungent hoppy aroma.
3)Taste: Is the beer sweet? Is it bitter? How does the taste fit in with the style. Again, an IPA should be very bitter to fit the expected characteristics, while some pale ales should be faintly sweet from carmelization.
4)Mouthfeel: How does the beer feel in your mouth. Is it thick? Does the flavor linger? Is there an aftertaste that should or shouldn't be there?
5)Alcohol: Does the beer reek of alcohol? Depending on the style this may or may not be desireable. Barley wine's for example have a very high alcohol content, as well as some porters. However, most beers shouldn't smell like Ethanol.
Well thats all for today. Hopefully that will get you started. Next I plan to delve into the basics or brewing. Hope you enjoyed today's installment!