Beers, as described in the Beer Judge Certificate Program (BJCP) style book, range from none to a puckering 120 International Bittering Units (IBUs). Some number crunching (standard deviation, and mean average) break these numbers down into some categories:
Lightly Hoped: 0-15
Moderately low hops: 15-25
Moderately high hops: 35-45
Highly hoped: 45 and up.
My preference is in the moderately low range, and my wife prefers lightly hoped beer. It's a fairly simple processes to find the range you like and calculate how much hops to use to achieve that same bitterness level. This can easily be done with various calculators found on the Internet.
However there is more to hops than just the bitterness level.
Over time as a brewer you will get a feel for the amount of bittering, flavor and aroma hops you prefer in a beer, but without that experience there is no way to really qualify or quantify what a beer may taste like given a recipe. In "Designing Great Beers" By Ray Daniels he gives a wonderful explanation of they wide variety of factors that play into flavor and aroma, compared to the relatively simple reaction the creates bitterness.
One simple way to quantify the type of bitterness the hops may add is to break them into two groups. Bittering and Flavor. Hops added early in the boil, spending more than 25 minutes in the kettle, will add mostly bitterness. Hops added later in the boil, spending less than 25 minutes will add mostly flavor. The ratio of bitter IBUs to flavor IBUs can be a way to compare recipes.
4:1 - mostly bitter.
2:1 - balanced.
1:1 - mostly flavor.
You'll also develop a sense of flavor for the various hops. My personal favorite is Challenger. It works wonderfully as but a flavor and bittering hop. Taste is very subjective, but if you keep this in mind with your brews you will be able to better evaluate hop schedules in recipes and better formulate your own recipes.
For more details on this subject this is a wonderful resource: