Ok, well, first off: there’s no "right" way to taste beer except with an open mind. Which is to say, don’t come to the beer with preconceived ideas of what you think you like, or what you think of the style, the brand, or the brewery.
That said, there are some key steps between pouring and drinking that'll help you fully appreciate your next pint.
The most important parts of tasting beer are to slow your approach, break things down, and build a vocabulary to describe what you're drinking. Take notes so you can vocalize what you like or dislike, and can have a record of your thoughts anytime you come back to the beer or compare it to something new. And as you taste, you'll start to find your palate, deciding what subtleties you like and what you don't.
You'll want to pay attention to these five points that form the basis of any beer evaluation, from the pros who judge competitions to off-the-cuff impressions of whatever you ordered at the bar.
Appearance
Put your glass up to the light and give it a careful look to note the color, clarity, and carbonation. Is the beer bright and clear, or is it more hazy? What color is it? Is there a decent head on top, or does the foam die down pretty quickly?
Smell
Aroma can hit you with a lightning bolt of memories, and is a huge component of tasting. Stick your nose deep into the glass and draw a deep breath. Let the beer warm up a touch, give it a good swirl, and then smell it again. Try to pick out any notes, however subtle — coffee, chocolate, caramel, spices, fruits, flowers, herbs, grains, anything like that.
Is it floral? Fruity? Roasty? Does it smell earthy, like a grassy field or pine-laden forests? Is there a musty, leathery note from the use of wild yeast? Do the hops or malts dominate?
Taste
This is what you’ve been waiting for. Take a sip and let the beer flow over your entire tongue, then note what you taste, from the beginning to the middle to the finish.
Is it sweet, bitter, sour, spicy, rich, or something else entirely? If it's a hop-forward style like an IPA, what notes can you pick out from the hops, like grapefruit, mango, grass, or pine? If it's malt-forward, like a stout or lager, what kind of flavors (dark chocolate, toffee, crackers, caramel, rye) do the grains give off? Keep sipping, trying to pick out new nuances as you go.
Mouthfeel
Is the beer thin and easy to drink, or rich and viscous for slow sipping? Is the carbonation biting, smooth, or tingly? Is the bitterness round and mellow, or sharply astringent?
Overall
This is the most important part. Do a quick recap of the steps above, and then — without thinking too hard — just answer this: Did you like it? If yes, what aspects were your favorite? If not, what didn't you enjoy?
Once you've got all that down, you should have a fully-formed opinion of what's in front of you. And then, of course, comes the best part: knocking back the rest of your pint.