This is roughly like saying "How do you play cards?". There is no one specific game of "darts". Darts are the implements used to play a whole host of games. They range from the very simple (Count Up - throw darts at the board, add the number you hit to your total score, keep going until someone hits an arbitrary number) to the complex (Cricket - each player must hit all of 15, 16, 17, 18, 19, 20, and the Bulls Eye, three times each, and then can begin collecting points for hitting it subsequent times, but only while at least one other player has not hit it three times each. First player to close all 7 number and have a higher point total wins).

Most dart rules share scoring methods in common, so I can give you those.
The numbers 1 through 20 are on the board, fairly randomly. 20 is on the top center. There is a bullseye in the center, with a circular scoring range surrounding it. The circular range around the bullseye is a Bull, and scores 25 points. The actual bullseye itself is a Double Bull, and scores 50 points. All the numbers have four possible scoring zones. The two large ones count the number itself. The outer ring next to each number is the Double zone, and hitting there scores double the points associated with the number. The ring between the Double zone and the Double Bull is the Triple Zone. Hitting that zone scores double the points associated with the number. Thus, the highest scoring zone on the board is NOT the bullseye as you might expect, but is in fact the triple-20, which scores 60 points.

Hope that helps!