After the first trick, the game continues in the same manner. The person who took the previous trick leads by playing the first card.
Let's suppose that the person who is leading the second trick places a diamond card face up in the middle of the table. The person to their left must also play a diamond card. Like before, there's an exception: if they do not have a diamond card, then they can discard any card in their hand. Since the first trick is over, they can play any point card on the trick. If they do this, it is called "breaking hearts", and sometimes people say that the person has "painted the trick". They can play the Queen of Spades if they have it, or any hearts card. They don't have to play a point card, however - they can discard a spade or club, any card is legal.
The first trick was described in a section above. The person who took the first trick has to lead the second trick. They are allowed to play any card in their hand except for a point card. This is rule #2: you cannot lead with a point card until "hearts have been broken". Suppose you are leading the second trick, and no one has yet taken a point card. You have some cards of each suit. You can lead with a club, a diamond, or a spade, but not a hearts card.
This rule is true for all tricks, not just the first and second ones. No one can lead with a hearts card until hearts are broken.
There's a drawback to this rule. If you are in the lead and all you have are the Queen of Spades and some hearts cards, and hearts have not yet been broken, then you are forced to lead the trick with the Queen of Spades! This usually results in the trick leader taking the Queen and her 13 points. It does take some skill to avoid becoming trapped in this situation. However, you may also get trapped into leading the Queen of Spades simply because of bad luck.
Most people play Hearts with the "Shoot the Moon" rule. A player who takes all the point cards during a hand has "shot the moon" - i.e. they have taken all the hearts cards as well as the Queen of Spades by the time all cards have been played. The result is that the other players are given a penalty of 26 points (in some cases, when it is beneficial, the player who shoots the moon subtracts 26 points from their own score). It is a matter of strategy to prevent other players from shooting the moon. In some cases, it may be strategically advantageous to let someone shoot the moon, or to help them to do so!
Shooting the Sun is similar to shooting the moon. However, it's even more unusual. If you take all the cards during the hand, point cards and non-point cards, then you've "shot the sun". The other players are penalized with 39 points [Edit: prior to February 2018, the sun penalty was 52 points].
Not everyone plays using this rule. It's more difficult than shooting the moon, and probably relies more on getting a particularly lucky hand.
The game continues as described above, until no one is left with cards in their hands. The total points collected by each player are recorded (1 point for each hearts card, and 13 for the Queen of Spades).
Then, the cards are combined into a single deck and reshuffled. The process is repeated as for the first hand of cards.
The game ends when at least one player has a score of 100 points or higher. The game is won by the person who has the lowest score. For example, if the players' scores are 55, 99, 101, and 110 after the last hand, then the player with 55 points is the winner.
Want to learn more about Hearts strategy? Take a look here: