Study the Scoring Elements
In order to be successful at mahjong you should study the scoring elements of your chosen style. You don’t need to memorize every single detail but you should be familiar with the general patterns, whether a patterns scores a few or a lot of points, and what constitutes a winning hand. When you are first dealt a hand recognize the potential combinations you can develop and shoot for them. Of course, your original plan may change (quite a few times) as the game progresses. This is why it is essential to know the scoring chart.
Pay Attention to Discards
As the game progresses try to guess what the other players around you are trying to collect. You can tell a lot about a player’s hand from their: 1) discards; 2) exposures; 3) tiles that they've never played. This is especially important to the player on your right, since he is the only player that can chow from you. Again this goes back to knowing the scoring elements. If you don't know the possible hands your opponents are going for you may end dropping the winning tile and that would spell disaster. Also pay attention for clues as to what players might discard in the future for your use, especially the player on your left.
Don't Meld Too Quickly
For a beginner not melding sets seems counterintuitive. If I'm one set closer to mahjong why shouldn't I take that chow/pung/kong? Well, there are several reasons why. If you begin too early by chowing and punging everything that comes your way you are often left with tiles that are often difficult to match up (and win) with towards the end. Another draw back from exposing your tiles too early is that anyone can see what you are going for and adjust their playing accordingly. An advanced player will pass up tiles so that his hand is flexible towards the latter half of the hand. Whereas, if you have everything melded you don't have too many options with the remaining tiles.