So here is what you should do.
When you start any game, you should look to be dominant early. This usually throws your opponents off in the first place. It's a good psychological trick for one. And of course, it puts you at a true advantage in terms of scoring.
Basically, you need to avoid the upper section scores because they're not going to do you much good so early on. Instead, go for your lower section scores. Try and hit a full house or a straight. Going the high scoring route early in the game is tactical, because if you need to take a zero in the game subsequently, you can take it on your upper section scoring, rather then lower section. If you've run out of the upper section boxes early in the game, you're in for a tough time!
Subsequently, start filling up the upper column as much as you can. If you start rolling a 4 of a kind, the lower section scoring opportunity is pretty low anyway. So you'd be better off taking it as a 4s or 5s, or any other combination. This is because if you hit 63 upper section points, you get a massive bonus of 35 points at the end of the game!
Lastly, you should try an aim for a Yahtzee at all times. Especially early in the game. It's a no brainer really. After all, it's worth 50 points. And if you get a consecutive one, you end up with a 100 more points.
If you were to roll a 3 or 4 of a kind, and you still have a roll left, you should definitely go for the Yahtzee. This is especially so if your upper section is such that you can fall back onto it. Further more, by leaving your 1s blank, you can take a zero on it anytime without feeling the pinch!
So there you have it. The Yahtzee strategy that has been laid out for you is extremely effective in winning games. You should look to adopt it into your own playing style!