In "How to Play Texas Holdem, Part 1 - The Set Up" I talked about a player's "Pocket Cards," the "Community Cards" and the type of rounds you'd find in a Texas Holdem game.
Here, I'll talk about how you bet during those rounds:
PRE-FLOP
After everyone has been dealt their 2 pocket cards, and no community cards have yet to be dealt onto the board, there is the first round of betting.
Starting with the player to the left of the Big Blind player, this player is often called "Under The Gun," he decides if he wants to continue in the poker hand by calling with the same amount as the Big Blind bet.
He also has the option of raising and betting more than this amount. As well, if he doesn't like the two cards that have been dealt to him, he can simply fold or muck them and the play continues clockwise to the next player.
When it is the Small Blind's turn, to play he only has to put in another half bet, because he had already put in a half bet before the pocket cards were dealt. If he folds, he is basically saying he is okay with losing the initial half bet.
If someone raises and puts in more than a Big Blind Bet, whoever is still playing their pocket cards has to match the current amount or re-raise it in order to stay in the game and play that poker hand.
Aside: "More on Raising"
Players can only re-raise each other in that round a maximum of 3 times before the bet amount is capped at the 3rd raised amount.
You'll often see players just calling the big blind, though. This is called "limping" into the pot.
THE FLOP
The betting is ended for "Pre-Flop" betting when all players have determined whether they will play with their pocket cards for the next round or not.
The next round is "The Flop." The dealer first "burns" a card face down in the "muck" pile and then flips over the next 3 cards.
Betting starts again with the first person still in the poker hand to the left of the Dealer.
THE TURN
After the "Flop Betting," the "Turn round is next. The Dealer burns another card and then flips over just 1 more community card alongside the 3 already dealt out.
Once again, another round of betting occurs.
THE RIVER
The River is the last round of a poker hand. The Dealer will burn another card again and place the last community card face up on the board.
This is also the last round of betting. At least two players still need to be in the pot for the poker hand to continue through the rounds.
Once all the betting is finished, any players still in the poker hand must flip over the cards to see who has the best poker hand.
The winner gets all the chips in the pot and this poker hand is now finished.

