There is an "easy" way to do this if you are drinking somewhere that uses fluid ounces instead of mL. I call it the "divide by 60" method.
A US "standard drink" is 12 fl oz of 5%. Multiplying 12 * 0.05 gives us 0.6 fl oz of alcohol as a "standard drink". However, since we are going to be using % alcohol over and over, I find it easiest to not do the conversion from % to decimal and just work with the % number. Then a "pseudo-standard" drink is 12 fl oz * 5 = 60.
Now you can calculate the "standard drinks" in your drink by taking the volume (in fl oz) multiplying by the alcohol percentage, then divide by 60. For example, a 20 fl oz glass of 6.7% IPA works out to 20 * 6.7 = 134. 134 divided by 60 is a little more than 2 (2.23 actually) and so your big glass of IPA is equivalent to a little more than two standard drinks.
Another example: a mixed drink with 3 "shots" of hard alcohol. In the US, a "shot" is roughly 1 - 1.25 fl oz. A lot of hard alcohol (vodka, gin, etc.) is around 40% alcohol. We can then calculate 3 fl oz * 40 = 120. Dividing by 60 gives us 2 "standard drinks" in your mixed drink. If you want to be on the safe side, you could round up: 3 shots * 1.25 fl oz = 3.75 fl oz round up to 4 fl oz. Then 4 fl oz * 40 = 160, divide by 60 to get 2 2/3 standard drinks.
I like this method because I find it somewhat easy (with a little rounding sometimes). I would probably need a calculator to use the other (good) methods that people have outlined in answers to this question, but I can do the "divide by 60" method in my head.