One of the main troubles that you can encounter when playing hearts is taking points that you never would have imagined you could possibly take-- imagine taking the queen of spades with a three of clubs! This can be absolutely devastating and can completely destroy not only the way that you intended to play your hand, but also your score. The key to playing hearts well and keeping your score low lies in being able to make these kinds of plays against your opponent while ensuring that nothing of the sort happens to you. The easiest way to do this is by creating a void, meaning that you have no cards in one or more suits (in this case, suits that are not hearts, as having a void in hearts isn't overwhelmingly helpful from a tactical point of view, since people generally do not lead hearts unless they're baiting their opponents or shooting the moon).
Look at your suits
The easiest way to have a hand with a void is simply to start the game that way; obviously, this is possible on every hand, but you only have direct control of it on the first through third hands (when you pass to the left, right, and across). When you first look at your hand, look for suits in which you have few or no cards. Pass cards that will allow you to have one or more suits in which you have no cards. This might mean passing lower numbered cards in diamonds while holding on to the cards with a point value, which are more often considered the dangerous cards to have in your hand. Sometimes, you may have at least four cards of each suit, in which case you can choose either to pass face cards and hearts (the standard tactic when playing) or try to create a lesser void in an suit.
The sooner the better
A void can also be created during play. Generally, the sooner you can create a void in a suit, the better, as you want to run out of a certain suit before everyone else at the table so that you can get rid of the cards in your hand that are worth points. If you don't run out of a suit until the fourth time clubs are lead, for instance, the chances are pretty good that someone else will have run out as well, which is fine for dodging the bullet when it comes to taking points, but it gives you less control over who you will give points to. The easiest way to create a void in a suit is to take control of the game early on (with a club of medium strength on the first hand, for instance) and then lead with low non-face cards in a suit in which you only have a few cards. This can be particularly useful when you only have one or two low-value cards in spades, as it will allow you to pull the queen into play.
Dump your worst cards
Once you have a void in a suit, you can sit back and wait for that suit to be led, and you will have the freedom to either get rid of high value cards in other suits (having an ace or king is always dangerous in Hearts) or sluff off some hearts that you have in your hand.