Pot-limit (usually abbreviated to PL) is a betting structure in which a player may bet or raise any amount between a specific minimum bet and the current size of the pot (see below for how to calculate the size of the pot). For this reason, a player cannot overbet a pot in a PL game.
Pot-limit games are usually described by stating the sizes of the blinds, in the form "small / big". For instance, a 1/2 PL game has a small blind of $1 and a big blind of $2. Sometimes, pot-limit games have maximum buy-ins, in which case a game may be described as "min buy in - max buy in" (for instance, a 100-500 PL game), but this is rare. Due to the inability for a player to overbet the pot, the main reason for restricting a player's initial buy-in is eliminated.
The minimum bet in a PL game is usually the size of the big blind; if it is any amount other than that, the game will explicitly state what the minimum bet is. Just as in no-limit games, raises which come after an initial bet in a betting round can be no smaller than the previous bet or raise, so as each bet or raise is made during a betting round, that bet or raise becomes the new minimum for that round. The minimum bet size is "reset" at the start of the next betting round.
Calculating the "size of the pot"
The most difficult part of pot-limit games is figuring out the maximum bet size. It involves simple math but is often difficult to do in your head. Even experienced players often cannot calculate the maximum bet size very quickly. The formula is:
Maximum Bet = (Amount Of Bet To You) + (Total Amount of Chips In Pot And In Previous Bets On This Round)
The Amount Of Bet To You is the amount it would take to call all previous bets in the current betting round. If there have been no bets before it gets to you, this amount is zero.
The Total Amount of Chips In Pot And In Previous Bets On This Round is the total amount of money already bet and in the pot; it's the amount in the pot from previous betting rounds, plus the sum of all current bets and raises in this round.
Some people find it easier to consider the first part of the equation as the equivalent of "first, calling the bet to you", followed by "betting the total amount now in the pot".
Because the math can be somewhat tricky to work out in one's head, especially if previous bet sizes haven't been clear, you may indicate you want to bet or raise the size of the pot by just saying "Pot", or "I raise the pot". If you're playing in a card room, the dealer can usually tell you the current pot size, and the amount you'll need to put in.
If a player is first to act on a betting round, then the amount of money currently in the pot is the maximum bet possible. So, in a 5-5 PL hold 'em game, if there is $20 in the pot after the flop, the first player to act could bet anywhere from $5 to $20 (or, of course, they could check). Let's say the player chooses to bet only $10. Subsequent players may choose to fold, call, or raise. A raiser would be allowed to raise any amount from $10 (that's a $10 raise, making it $20 to go) to the size of the pot, which in this case is $10 (the amount of the bet to you) + $30 (the total amount of chips in the pot, including the current bets), or $40. Again, that would be a $40 raise, making the total bet $50. Let's say this second player chooses to raise the maximum, so it's now $50 to go.
If a later player wants to raise the pot, you do the same math. They may choose to fold, or call the $50 bet to them, or raise. If they raise, the minimum amount they may raise is $40 (the amount of the previous raise). The maximum amount they may raise is $50 + $80 (the amount of chips in the pot is the original $20 in the pot from previous betting rounds, plus the original bettor's $10, plus the second bettor's $50, for a total of $80), or $130. Again, that is the maximum amount they may raise: if they do so, they will be making it $180 to go (raising the current $50 bet by $130).