Here are strategies for winning at Hearts. Although, like any card game, there is some degree of chance involved, there is also a large element of strategy and a smart player will find himself at an advantage over less informed, novice opponents.
One of the most important strategies is knowing how to pass. As a general rule, you want to get rid of the most dangerous parts of your hand and, if possible, short suit yourself (i.e., no cards in one suit) of clubs or diamonds. (However, you may get other cards in that suit passed right back to you by an opponent who also wants to shortsuit himself of it.)
Never short suit yourself of spades below the Queen; always keep spades valued Jack or lower. If you have four or more low spades, then you don't have to worry if you have any of the high spades and should concentrate on discarding another suit.
The most dangerous cards are the Queen, King, and Ace of spades. They become increasingly more dangerous the fewer low spades you have, because if someone leads spades more than a few times you'll have to play them and likely take the Queen. High hearts are also dangerous if you do not have low hearts as well (2-6), and should probably be passed on. Keeping low hearts can actually be advantageous because if anyone leads a heart, you can play a low one and not win the trick.
Bear in mind that you do not always have to pass on the Queen if you have it. If you are rich in low spades, it is safer to keep it, because you always know where it is and have control over when it is discarded. If you do pass the queen, remember to whom you passed it. If, on a trick, you play after him, you can safely take the trick without risking taking the Queen.
An interesting strategy is to pass on the 2 of clubs if you have it. Because that card always starts the game, and the first trick is safe from any point-taking, not having to lead the 2♣ allows you to play a high Club (which you may receive from the other player) "safely".
Pay attention to the cards passed on to you; they might reveal something about your competitor's hand. If you get lots of cards of one suit, that usually means the opponent wants to shortsuit himself of the suit. Receiving the Queen might mean he's low on Spades. If you get suspiciously low, unimportant cards, that might suggest he's trying to hoard all the strongest cards and shoot the moon, which you should consider taking your own steps to defend against (see the Shooting the moon section below).
An elementary strategy in Hearts, as in many Whist-family games, is to void or short-suit a particular suit in their hand; that is, to have very few or no cards of that suit in their hand as play begins. Voiding may be done by passing cards or through play of the first few tricks, or a combination. By voiding a particular suit, when that suit is led you may play any card you choose; you may try to void another suit, or you may play dangerous cards (like the AKQ♠, high Hearts, or face cards of any suit) to get rid of them, in the process possibly foisting off penalty points on another player. By voiding or shorting a suit, you also usually guarantee that someone else will be "long" in the same suit (having many cards of the suit in their hand), which can force that player to take a lot of tricks (and points) if they are forced to lead their "long" suit late in the game after everyone else has voided it. Voiding a suit as early as possible is thus extremely beneficial.
You should NEVER attempt to void Spades by passing them. As stated in the previous section, unless you happen to have the AKQ♠ and no others, there is a chance you may receive one of those cards from another player and be stuck with it as your only Spade (a dangerous situation, as flushing is a very common tactic; see below). It is usually never a problem to be "long" in Spades, especially low Spades, unless your hand is so long (i.e. 8 or more Spades) that it may indicate someone else is already very short or void in them (and so can play penalty Hearts that you may take even with a low led Spade). Voiding Hearts is less risky, but again unless you have only high Hearts it's usually better to save a few low to middle Hearts (especially 2345♥) to guard against being passed a high Heart (and then being forced to "eat" it, possibly with others).
Most players will attempt to void Diamonds and/or Clubs if they are fortunate enough to be dealt a hand with no "risky" cards like high Spades, Hearts, or Aces/Kings. Short-suiting Clubs in order to void them early is a good bet in the most popular ruleset, where the 2♣ must be led on the first trick and Hearts cannot be broken on that trick. By having only one or two Clubs, you can void them in a relatively safe manner early in the game. Diamonds are commonly voided where possible because, unlike Clubs where players will play their highest cards on the first trick to "safely" get rid of them, there are no "safe" Diamond tricks; any trick in which a Diamond is led could have a Heart played on it if a player has managed to void the suit. However, if playing with the common J♦ variant (where the J♦ removes 10 points from your score), voiding Diamonds means you will be unable to capture the J♦ (with this variant in play it is extremely unlikely that a player will simply "sluff" the J♦ off-suit to another trick, unless trying to feed it to another player like the last-place player).
When you're leading a trick early in a round, your priorities should be to either shortsuit or, if you don't have the Queen, King, or Ace of spades, force the Queen to come out by playing lower spades repeatedly (a tactic known as flushing).
If you have the Queen and want to shortsuit yourself, lead with the suit you want to shortsuit at every opportunity, starting with high cards. Because nobody can discard the Queen to you, the worst you can do is collect a heart or two, which is far preferable to taking the Queen.
If you are the last player to play in a trick and you realize you will have to take it no matter what, play the highest card you can. This way, you get rid of a high, potentially dangerous card, without any further damage.
Being able to lead in the first few tricks of a round is generally useful to help control the pace of the game, but remember that as a round progresses, there will be fewer cards left, and it will become increasingly likely someone will be short-suited. Thus, if you end up leading in the last 2-3 tricks of a round, and have cards of only one suit that the other players are out of, you might be "stuck" with the lead, even with very low cards that would normally be safe. This danger can be avoided by opting not to win tricks when the players have fewer than 4 or so cards apiece, wherever possible. You can also try to "plan out" your plays in the early part of the round so that you'll have low cards in 2 suits left towards the end, thus lessening your chance of being stuck.
Keep track of the cards played
This is a no-brainer. In an ideal world, you would remember all the cards that have been played, but in practice this is not feasible for most people, so it's better to limit yourself to the most important ones.
Obviously, keep a sharp eye on when the Q♠ comes out, and have a general idea of how many hearts remain (see below section). It's also highly useful to remember when the QKA in clubs and diamonds have been played, so you can determine whether your J♣ is now the most powerful card in that suit, or whether there's still a possibility that someone else will win the trick with a higher card. The lower cards in each suit (2-9) aren't usually worth memorising, unless you're trying to shoot the moon. (More on this later.)
On the first hearts trick after hearts are broken, somebody will most likely lead a low heart, like 4, 3, or 2. If you are leading, lead low. The other players will use up their low hearts trying to lose the trick. If you lead a middle card, it is likely you will get the hearts. On the second heart trick, it is usually safe to lead a middle card, like 5, 6, 7, 8 because the lower cards have been used up. To get rid of the high hearts, discard them on other tricks.
Avoiding the Queen
The two and most apparent rules to avoid the Queen are to either avoid having the King and Ace of spades or to get rid of them as quickly as possible by either discarding or playing them when all the other players have already played. You will not have to worry about them if you have a long suit of spades or you have the Queen of Spades, though it may still be useful to get rid of them as they are high cards. In the passing you should never throw away spades below the Queen of Spades.
However, there is one thing you need to watch out for. If people are dealt or passed the QS short (i.e. with few other spades,) they will try to shortsuit and play the Queen when someone leads the suit. This is a good reason not to lay high cards after the first two or three tricks, unless you are shooting the moon and want the Queen or are the last person in the lineup and the QS hasn't been played.
Getting the Jack
To get the Jack of Diamonds, which subtracts 10 points from your score, you should keep your high diamonds. If you have the Jack, you should not pass it away. While playing, when someone leads a diamond, play one of your lower diamonds. If the Jack appears, you should take it with one of your higher diamonds. If you have the Jack, do not lead it unless all of the higher diamonds have already been played. You will not get the Jack by leading other suits because the holder of it will obviously not discard it unless he is forced to, on the last trick.
Shooting the Moon
Shooting the moon is when you want to win all the hearts and the Queen of spades. If you succeed, you gain no points that round and every other player gains 26 points (in some circles, you have an option to instead take 26 points off your score). A variant is Shooting the Sun, when you win all of the tricks, then the other players get 52 points. This is a very dangerous thing to attempt, because if you miss taking even one heart, you get a very large sum added to your score.
It's difficult to shoot the moon without most of the high hearts (10-A) and a long suit. If you have 7+ cards in one suit besides hearts, including an ace and at least two other high cards, you should consider going for it. Try to trade off low cards in a suit you don't have much of. When someone leads the suit you have a lot of, make sure to win the trick and then repeatedly lead with your highest cards in the strong suit. If pulled off correctly, everyone will eventually run out of that suit and you can win every trick you lead with the suit, even with low cards.
If you suspect that someone else is trying to shoot the moon, you can try to stop them by saving two or three stronger cards for the last tricks, so you can snatch a few hearts away (remember, the loss of one single heart foils a moon-shot). A good indication someone is trying to shoot the moon is if he passes you very low cards that usually aren't considered dangerous, or if he begins repeatedly leading with high cards of one suit once the trick-taking has started and doesn't seem to be cautious about avoiding hearts.