How does betting work in Texas hold'em poker.  More specifically, I
understand that there are a number of rounds of betting but when does
the first round finish enabling the flop to be dealt and when does the
second round finish to enable the turn to be dealt etc

The betting rounds ends when no one raises the bet, and when the pot
is even all the way around, or those that can't/won't match the bet
fold.

A Texas Hold em poker game goes as follows:
http://www.texasholdem-poker.com/beginnersintro.php

..."

1. The betting structure can vary. Sometimes antes are used, but most
games start with two players to the left of the dealer placing out a
predetermined amount of money so there is an initial amount to get
things started. This is called posting the blinds. Click here for more
info on blinds and antes.

2. The dealer shuffles up a complete deck of 52 playing cards.

3. Each player is dealt two cards face down. These are called your
hole or pocket cards.

4. Then there is a round of betting starting with the guy to the left
of the two who posted the blinds. This round is usually referred to by
the term pre-flop.

5. The amount a player can bet depends on what kind of game it is.
(Click here for more information about betting structures)

6. Much like most games of poker, players can check, raise, or fold.

7. After the betting round ends, the dealer discards the top card of
the deck. This is called a burn card. This is done to prevent
cheating.

8. The dealer then flips the next three cards face up on the table.
These cards are called the flop. These are communal cards that anyone
can use in combination with their two pocket cards to form a poker
hand.

9. There is another round of betting starting with the player to the
left of the dealer.

10. After the betting concludes, the dealer burns another card and
flips one more onto the table. This is called the turn card. Players
can use this sixth card now to form a five card poker hand.

11. The player to the left of the dealer begins another round of
betting. In many types of games, this is where the bet size doubles.

12. Finally, the dealer burns a card and places a final card face up
on the table. This is called the river. Players can now use any of the
five cards on the table or the two cards in their pocket to form a
five card poker hand.

13. There is one final round of betting starting with the player to
the left of the dealer.

14. After that, all of the players remaining in the game begin to
reveal their hands. This begins with the player to the left of the
last player to call. It's called the showdown.

15. The player who shows the best hand wins! There are cases where
players with equal hands share the winnings. Click here for more info
on who wins and about split pots.

..."


Good Luck!   --I hope this helps.

Well, it depends on whether you are playing limit hold'em or No limit
Hold'em.  In a limit game there is a cap:

"...The Cap: In Fixed limit games, each round of betting can consist
of one bet and has a maximum number of three of allowable raises,
known as the cap. So, if a bet is made, that bet can only be raised
three times, after which all players must call, or fold. However, if
only two players remain in the hand the cap is increased, to a maximum
of five raises..."

http://www.bodog.com/poker/guide/rules-texas-holdem.jsp

In a no limit game betting continues as described by cynthia-ga.

When to Stay in Texas Hold'Em

**In texas holdem, much depends upon the first three cards. Unless you
have something to start with, you're not apt to have anything
worthwhile at the finish. There are some optimistic players who argue
against this texas holdem strategy, but the law of averages is against
them. They look at it this way. If you take three aces, shuffle them
in with four odd cards and deal them out, you will still have three
aces, regardless of the order in which they turn up.

That is very true, but the texas holdem strategy doesn't hold with
seven cards taken at random, since there is no guarantee that three
aces will be among them. Surprises do pop up in the final cards of a
seven card deal, but not as often as people think. They are inclined
to remember such hands and overlook those that turned out to be a
total bust. So a hand that starts out with good cards is really the
only type of hand to play and a good texas holdem strategy to follow.

That raises this texas holdem strategy question: just how good should
the first three cards be? The answer to that texas holdem strategy
question depends to some degree on whether the game has a high or low
limit, as well as the type of players involved. Keep this in mind --
if you play a tight game when everybody else is taking chances, some
of your best hands may lose out, because of the chance of surprise
hands cropping up. So you might as well get in the swim yourself,
though not too deeply.

Since we have mentioned three aces, we may as well mark it as the
ideal holding to start off a hand of texas holdem. With two aces as
hole cards and a third as an up card, you are likely to have the pot
won then and there, since the average winning hand in texas holdem is
probably around three nines. The presence of an ace as an up card does
not give away the fact that you have two others in the hole; in fact,
it may create the impression that your other cards are not too good
and that you are counting on a lone ace to bolster them. However, but
the time five or six cards have been dealt, with no other aces
appearing among them, other players may suspect that your hand is
better than they thought.

You can also visit: http://www.poker-authority.com for more online poker tips.