Strategy

The strategy of dominoes can be broken down into three categories:
1. Scoring
2. Preventing your opponent from scoring
3. Blocking
These are listed in order of increasing difficulty, and therefore are charactersitics of domino players of increasing ability.

Scoring

There are certain "magic" or "repeater" dominoes which you should try to hold on to because they make scoring easier. If your opponent has just scored, then you won't be able to score without one of these, and if you score, it then makes it more difficult for your opponent to score. These dominoes are the 0-0, 0-5, 5-5, and 6-1. If your opponent scores with a blank, five, or a non-double six or one on an end, then you would also be able to score with one of these.

Other magic dominoes can score when there is a double on an end. These are the 1-2, 2-4, and 3-6, which can duplicate the points in a 1-1, 2-2, and 3-3. Other magic dominoes are the 3-1, 4-3, and 6-2, which will score five fewer points after a 3-3, 4-4, and 6-6, respectively.

Preventing your opponent from scoring

After you get good at finding scoring tiles in your hand, you will be able to start looking for potential scoring plays that your opponent could make, and play ones from your hand that give him the least opportunity.

Blocking

The simplest form of blocking is achieved by noticing when your opponent is forced to draw from the Bone Yard, and making a mental note of which numbers he could have played to. Then, try to make those numbers his only options again.
You can also consider that if you have several of one number, or if several have already been played, your opponent is more likely to be out of them.
Another strategy related to blocking, is to use your low dominoes to try to force the low dominoes out of your opponents hand, then when you go out, he will have more points left in his hand. Try to remember to use your larger dominoes for scoring, and your smaller ones for blocking.