HighCard Points. The quickest way to determine the strength of your hand is to count the highcard points (HCP). Here's how it works:

Distribution Points.
It is also common to count extra points for good distribution. The simplest method is counting points for short suits:

Problem Suits.
Certain combinations of high cards are worth less in short suits:

My recommendation for such suits is:
In a "problem" suit, you may count either HCP or distribution, but not both. 
For example, a KQ doubleton is worth 5 points (for the K and Q), and a J singleton is worth 2 points (for the singleton).
Points Required for Game.
Here is the approximate number of points you and your partner need to make various game contracts:

Note that only HCP are helpful for notrump: since you cannot trump anything, short suits are not an asset in a notrump contract.
The basic scoring formula is as follows:

NOTE: For most contracts, your score depends on what you make, not what you bid. For example, 1 making 3 and 3 making 3 are both worth 140 (50 + 3 × 30). The exception is game contracts: you must bid and make a game contract to get the 250 point bonus.