Almost everyone has been bowling, but do you know how to keep score if there isn't a computer there to do it for you? It's pretty simple, and I will explain the rules here along with an example of a real game.
Above is a bowling score calculator. You can enter in values to simulate a game and click "Calculate Score" to see the results. To test your scoring abilities, you can enter in the score for each frame in the bottom row of textboxes to see if they match the actual scores.
If you knock down all 10 pins in the first shot of a frame, you get a
  strike.
  How to score: A strike earns 10 points plus the sum of your next two
  shots.
  
Spare
If you knock down all 10 pins using both shots of a frame, you get a spare.
  How to score: A spare earns 10 points plus the sum of your next one
  shot.
  
Open Frame
If you do not knock down all 10 pins using both shots of your frame (9 or
  fewer pins knocked down), you have an open frame.
  How to score: An open frame only earns the number of pins knocked down.
  
The 10th Frame
The 10th frame is a bit different:
  If you roll a strike in the first shot of the 10th frame, you get 2 more
  shots.
  If you roll a spare in the first two shots of the 10th frame, you get 1 more
  shot.
  If you leave the 10th frame open after two shots, the game is over and you do
  not get an additional shot.
  How to Score: The score for the 10th frame is the total number of pins
  knocked down in the 10th frame.
  
  Frame 1:
  You got a spare. Your score is 10 plus the number of pins you knock down in
  your next shot. In this case it is 5, so you have 15 points in Frame 1.
  
Frame 2:
  You have an open frame of 9 points. Add 9 to your previous score (15), and you
  have 24 points in Frame 2.
  
Frame 3:
  Another open frame of 9 points. Add 9 to your previous score, and you have 33
  points in Frame 3.
  
Frame 4:
  Strike! You earn 10 points plus your next two shots. In this case, your next
  two shots are a strike and a 5 which is a total of 15 pins. So, 10 + 15 = 25
  points earned for Frame 4. Add 25 to your previous score, and you have 58 in
  Frame 4.
  
Frame 5:
  Strike again! You earn 10 points plus your next two shots. In this case, your
  next two shots are a 5 and a spare (another 5), which is a total of 10 pins.
  So, 10 + 10 = 20 points earned for Frame 5. Add 20 to your previous score, and
  you have 78 in Frame 5.
  
Frame 6:
  Spare! You earn 10 points plus your next shot. In this case it is 5, so you
  have 15 points in Frame 6. Add 15 to your previous score, and you have 93 in
  Frame 6.
  
Frame 7:
  You have an open frame of 8 points. Add 8 to your previous total, and you have
  101 in Frame 7.
  
Frame 8:
  You have an open frame of 9 points. Add 9 to your previous total, and you have
  110 in Frame 8.
  
Frame 9:
  Spare! You earn 10 points plus your next shot. In this case, your next shot is
  a 9, so you have 19 points in Frame 9. Add 19 to your previous score, and you
  have 129 points in Frame 9.
  
Frame 10:
  Last frame. You got a spare in the first 2 shots, so you roll again and get a
  strike. Remember, your score in Frame 10 is the total number of pins knocked
  down. In this case, you knocked 20 pins down. Add 20 points to your previous
  score, and you have 149 points for the game!