When it comes to playing Hearts, once you've made your passes you have to play your cards as best you can. While shooting the moon (getting all 26 points) is possible for experienced players, these beginner tips will presume that you are not trying to shoot the moon, and are just looking for some basic Hearts strategy tips.
The First Trick
There aren't many options here. If you have the Two of Clubs, you're leading it. Since no points can fall on the first trick, play your highest club. If you are void in clubs, then use the opportunity to trash an otherwise dangerous high card (like an Ace or King of Spades), or try to void yourself in a second suit. More voids mean more opportunities later.
Generally speaking, after the first trick falls, any player who is not in danger of taking the queen of spades will want to lead spades as much as possible. The main theory behind this is simple: if spades keep being led, the players with the A, K and Q will eventually have to play them. If you're not holding any of those cards, you want to force them into play as soon as possible, so someone else gets stuck with those 13 points.
If you fail to bleed spades, the player holding the queen may be able to create a void in another suit (such as clubs or diamonds) and then dump the queen on an off-suit trick. Unless you are holding a near-perfect hand with no high cards likely to win any tricks, your battle plan should probably involve leading spades as much as possible until the queen has fallen on someone else.
Conversely, if you are stuck with an undefended Q, K or A of spades, you are in danger of taking the queen if spades keep being led. Your goal should be to create a void as soon as possible, by leading suits of which you only have one or two cards. By dumping your only two diamonds, for example, you can hope that someone else leads diamonds and allows you to drop your bad spade.
If you are holding the Queen of Spades, another option is to lead your longer suit (clubs or diamonds) and hope someone else is void. Since you hold the Queen of Spades, the worst that will happen is that a few heart points will fall on you. Once this happens, hearts will have been broken, and people may lead hearts instead of spades. If you have few hearts and can dump the queen on a hearts trick, this is ideal.
These are the bad cards. Once you avoid the Queen of Spades, you want to try not to get many of these. Sounds easy, right? Well, it depends on what cards you have in your hand. If you have low hearts, you don't have to worry, since you can duck under any hearts lead. If you're holding high hearts, you want to try to dump them on someone else as soon as possible, and not lead hearts.
If you can create an early void by getting rid of all your cards of a single suit, you should almost always do so. Doing this means that the next time that suit is led, you can get rid of your worst card, which is a very powerful position.
Likewise, it's important to keep track of other players at the table who have voids, so you don't lead a suit with which you might get stuck.
While not strictly necessary to play Hearts, you will do a lot better if you can keep track of how many of each suit has been played. This is less difficult than it might sound; until someone reveals a void by dumping an off-suit card, the number of cards played of any suit will be divisible by 4.
This is important information to keep track of to avoid playing into other players' voids. For example, if three full rounds of clubs have been played, and you have a club in your hand, it is the last one. Leading it will let everyone else dump cards on you.