A betting action is an action a player can take when it is their turn in a betting round. Players may take only one action when it is their turn.
The six types of betting actions are:
To choose not to bet (can only be done if no player has bet before you, or if you had a forced bet which is equal to the amount of the bet that comes to you).
To be the first player to place an amount of money into the pot. The amount of money you may place into the pot is regulated by the betting structure of the game you are playing.
To match an earlier bet amount.
To match and increase an earlier bet or raise amount. The amount of money by which you may increase the bet or raise depends on the betting structure of the game you are playing.
To discard one's cards and leave the hand. Generally this is only done if there is a bet in front of you and you do not wish to call, but there is no rule preventing a player from ill-advisedly mucking her cards in turn instead of checking.
To raise a previous partial bet to a "full bet". This is a rare action, since it requires a partial bet be in front of the player making the action.
A commonly-heard seventh action is to "re-raise", but this is nothing more than a raise being applied to an earlier raise (as opposed to raising the original bet). Some players incorrectly use the phrase re-raise whenever they raise, but it technically can only be applied if you are raising an earlier raise of an earlier amount. Re-raising is not a term that is required to be used at all; it is also correct to simply say you are "raising" if you are raising a previous raise; though it is sometimes helpful to clarify for a dealer that you are intending to raise the raise -- otherwise the dealer may think you have simply not heard the earlier raiser and are trying to raise the original bet.
When it is your turn to take a betting action, you have at most only a few seconds to take the action. Since most players have made up their minds almost immediately upon seeing their cards, this is usually not a problem, but if you require more time to make a decision as to your action, you should ask the dealer for time, by merely stating "Time", out loud.
In a brick-and-mortar casino, if you do not take action in 3-4 seconds but do not ask for time, dealers may mistake any particular word you say or motion you might make with your hands to indicate a check, since so many signals can indicate checking. If the dealer is distracted momentarily, and other players later in the betting round appear to act before you, the dealer may simply assume you checked and will take it for granted that you have done so. If you see a player after you act, and you have not yet acted, point this out to the dealer (and to the player) to ensure that you still have opportunity to act. Players after you acting before you are said to be "acting out of turn", and it is not only considered rude, but can also have binding consequences.
In online casinos, typically you don't have much time even if you "ask for time," and in most games you cannot ask for time at all. They often give a default amount of around 20 seconds or so for any given player, but expect you to make the decision in five seconds - anything longer and the software will usually start beeping at you, in case you've fallen asleep at the keyboard.