Counting them
There are 52 cards. You can see six of them — your two and the four on the board — which leaves 46 you cannot. An out is one of those 46 that gets you where you need to go.
Say you are holding two hearts and two more are on the board:
Thirteen hearts exist. You are looking at four of them, so nine are unaccounted for. That is the number.
The counting is always this literal. Work out which cards finish the hand, then subtract the ones already face up.
The counts worth memorising
A few board textures come up constantly, and knowing them saves you the arithmetic every time.
Learn them, then be suspicious of them. They are answers to specific board textures, and reaching for one without checking the board in front of you is the second-most-common way to be wrong.
Turning outs into a probability
A count is not yet a decision. With one card still to come, each out is worth roughly two percent:
Nine outs is about 18%. Eight is about 16%. Four is about 8%. The real numbers are a shade higher — nine outs out of 46 unseen cards is 19.6% — so the shortcut is slightly pessimistic, which is the right direction for a shortcut to err.
Now the two halves meet. If a half-pot bet needs you to win 25% of the time and your flush draw gets there 18% of the time, the call loses money. Nine outs is not enough at that price. Against a quarter-pot bet, needing 17%, the same draw is a call.
The two ways to get it wrong
As with Pot Odds, the wrong answers in the game are specific errors rather than arbitrary numbers, so a miss tells you something.
Counting only the cards that make exactly that hand
If you are drawing to a straight and the board pairs your ace, the card that makes you trips also saves the hand. Anything that reaches the target or passes it counts, so count the improvements you did not plan for.
Using a memorised count from a different draw
Nine is the answer for a flush draw with four suited cards visible. It is not the answer for a flush draw where one of your suit is already on the board twice over, or for a board that is not a flush draw at all. Count the board in front of you.
What counting cannot tell you
Every out here is a card that improves your hand. Whether the improved hand actually wins is a different question, and it depends on what the other player has. A flush that arrives on a paired board can be second best. Treat the count as an upper bound on how often you are saved, then discount it for the times you improve and still lose.
For the other half of the calculation, see pot odds.