LIMIT HOLD 'EM: Popular in casinos. The betting is fixed. Bets and raises during the first two of the four rounds of betting - pre-flop and flop - must equal the big blind. In the Turn and River betting rounds, bets and raises must equal twice the big blind. Example: the table is $4/$8, where the small bet is $4 and the big bet is $8. Blinds are half - small blind is $2, big blind is $4 (always equal to the small bet). In the pre-flop and flop rounds, the first bettor can only bet $4 and the next person could raise to $8 and a re-raise would be $12. In the Turn and River rounds, betting is in increments of the big bet, $8, $16, etc.
NO-LIMIT HOLD 'EM: Popularized by televised tournament poker. Size of cash games are determined by the size of the blinds. Buying in could range, for example, from 20-100 big blinds. A $5/$10 game would cost $200 minimum for a chair at the table. In no-limit, the betting/raising range goes from the table minimum (big blind) to all of a player's chips (going "all-in"). The minimum raise equals the size of the previous bet or raise. A re-raise must be at least equal to the previous raise. At any time a player can move in all the chips they have in front of them. Example: If the last bet was $5, the minimum raise is $5 bringing the total bet to $10. Maximum is all-in.
POT-LIMIT HOLD 'EM: This one is in the middle of limit and no-limit - a player can't bet all of their chips, but they can bet a maximum of whatever's in the pot at the time of the raise. Minimum bet is the size of the big blind and maximum is the size of the pot.
Example of a minimum raise: Player A bets $10. Player B calls $10 and raises $10 (total bet of $20). If the big blind is $5, Player B cannot bet or raise $5. They must match the amount of previous bet or raise in the same round.
Example of a maximum raise: The pot is currently $100. The size of the pot is determined by the active pot plus all bets already on the table and the amount the active player must call first before raising. Two scenarios: (1) The pot is $100 and Player A checks. Player B can raise up to $100. (2) The pot is $100. Player A checks. Player B raises $100. New pot total $200. Player C must call Player B's $100 raise first, bringing the new pot total to $300. Player C can then raise up to $300 (total bet with $100 call and $300 raise = $400).
Pot-Limit Hold 'Em is not as popular as the limit and no-limit versions, but Pot-Limit Omaha is gaining in popularity, so you'll have the tools to play a new variant once you familiarize yourself with pot-limit.