There are three main betting structures in poker: Limit, No Limit and Pot Limit.
Limit games have set amounts that you can bet during each round. For example, a $2/$4 Limit Hold 'em game would allow you to bet in $2 increments pre-flop and on the flop, and in $4 increments on the turn and river. Sometimes you will encounter spread limit games (common in Stud) that allow you to bet in a certain range. For example, you may get involved in a $1-$5 Stud game. On any street, you can bet $1 to $5. If you choose to raise you may raise up to $5, as long as you raise at least the amount that was previously bet. There is usually no cap on the amount of money a player can buy in for, and the minimum buy-in is normally ten times the small blind ($20 in a $2/4 game).
No Limit games have a fixed blind amount, but the players are able to bet any amount from the minimum bet (typically the size of the big blind) up to their entire stack at any time. Most no limit games have a minimum and a maximum buy-in, the minimum typically being 20 big blinds and the maximum usually being 100 big blinds. For example, in a game with $1/$2 blinds, the buy-in range would be from $20 to $100. If a player drops below the maximum buy-in, they may add on to their stack to bring it back up to the max buy-in. Raises must be equal to or greater than the previous raise, unless a player is raising all-in.
Pot Limit is very similar to No Limit, in that there is typically a minimum and maximum buy in, and players betting is not limited to a specific structure. Bets can range from the minimum bet (the size of the big blind) up to the size of the pot. Pot size is equal to the amount of the bets in the middle, all bets out on the table, plus the amount a player must call before raising. For example: if the pot in the middle of the table is $20 the first player acting the round bets $10, the next player to act is able to bet a maximum of $40 - $10 for his portion of the call and raise by $30.