So in this post, I'll explain some really basic principles about determining your chance of winning a hand based on the information you have at a specific point in time. Being able to determine if you should make a call, or even raise without the goods, but having a really high potential can really improve how you play. For example:

Your down cards are:  You've limped into a pretty good sized pot with 2 or 3 other players.

The flop looks like this:

   Here's how to figure your precentage of winning the hand. Some of this is kind of subjective, you have to determine if your opponent is on a flush draw, or maybe they have a big King. So the first thing to do is determine which cards will give you a winning hand, in this case a fair assumption is a straight, or a flush to win. (it would be a low flush, but the possibility of 2 people having 2 diamonds is pretty low).

   Count all the cards that would make your hand

            In this case there are 9 other diamonds that would help.
            There are 4 aces in the deck that would make a wheel.
            There are 4 sixes in the deck that would make a straight.

            So you have '17' cards to make a really good hand.

            When the board has three cards, you times your outs by four.

            17 X 4 = 68 - So you have a 68% chance of hitting one of those cards.

So if nobody goes crazy betting, it's a good place to put in a good raise, or just call if you're lower in chips.
Say the next card to come is a 'blank' (a card that does not improve your hand like )

            Now when the board has four cards, you still have the same amount of 'outs' times it by two now.

            17 X 2 = 34% - Your odds are drastically lower, but 3.4 times out of 10 you'll still make your hand!

So the river finally flops, and you've caught the . This is called having the 'nuts'. There is not a single hand that can beat you. You're praying that someone was slow playing the , flush, and you'll be able to get all their chips. Having a powerful hand like this all you need to worry about is extracting the highest amount of chips from your opponents as possible. Sometimes this is a great place to check (fake weakness) and let someone do something stupid like move all in w/ their flush, or high pair.

The other portion of this to consider is pot odds. This gets in to a way more complex discussion, but the base theory of pot odds is putting your money in at the right price. Let's say the pot has 10,000 in chips, and someone makes a $2,000 bet. You only have $4,000 in chips left. If you have the hand mentioned above, w/ a 64% shot at it, you're compelled to call, here's why.

      $10,000 + $2,000 = $12,000 So by you adding your $2,000 to the pot, you could win $12,000 for the mere $2,000 investment 12/2 = 6, your're getting 6 chips for every 1 you put in. That is essentially what pot odds are.

Another scenario: The pot is $4000, you have $20K in chips, the chip leader of the game just moved all $30k of his chips into the pot, you have a pair of fives. Do you call? Probably not, as I understand pot odds, you generally want to be getting 3:1 on your money at least to call with a marginal hand like pocket 5's.

   $4,000 + $20,000 (you only have 20k left, so you can only win what you put in) = $24,000

So you're talking about risking $20,000 to win $24,000, it's your tournament life at stake here, you're getting 1.2 : 1, generally most people would fold almost every hand other than pocket aces (AA) or pocket kings (KK). If you know the person betting is reckless, or bluffs a lot, it may be ok to make the call, but realize you'll be in a race situation, meaning you're lucky if you have a 50% shot before the cards are dealt.

This site offers a GREAT odds calculator.