Keeping score in a game of bowling may seem complicated, but it really just comes down to adding up the number of pins each player knocks down. Each frame, a player has two opportunities to knock down ten pins. A game consists of ten frames, and the player with the highest score at the end of the tenth frame, wins.
If you are bowling at an alley without a scoring computer, you'll probably be given a paper scoresheet. Before you start playing, record each players name in the appropriate area of the scoresheet. The pins that are knocked down on a player's first attempt are counted and recorded. The mechanical pin setter then removes the standing pins, clears the knocked-down pins, and then returns the remaining pins.
The player then takes their second attempt, and any additional pins that are knocked down are counted and added to the first. The score from both attempts is first added together, and then to any previous scores, to calculate the running score for the frame. Most scoresheets have a small area in each frame to record the number of pins knocked down in each of the first and second attempts. The running total is then written in the larger area of the scoresheet.
If a player knocks down six pins on their first attempt, and then two pins on their second attempt, then they've scored an 8 on the first frame. In the second frame, if that player knocks down seven pins on their first attempt, and one pin on their second attempt, then their total score is now 16.
Players score bonus points when they knock down all ten pins in a frame, by either bowling a strike or a spare. The number of bonus points depends not only on whether a strike or spare was bowled, but also on the player's performance with the next 1 or 2 balls.
You score a strike when you knock down all ten pins on the first ball of the frame. To record a strike, mark an X for that frame; their score will be the ten pins of the strike plus any pins knocked down on two balls of the next frame. (You delay recording the score for that frame until the next one is completed).
After a strike, the next frame should be scored as usual. If the player bowls a second strike, scoring will need to be delayed until the next frame. The pins knocked down with that ball are added to the 10 from each strike.
A player that knocks down all 10 pins with their second ball is scored as rolling a spare.
To record a spare, mark a/ in that frame. The score for the frame is the 10 pins knocked down plus the number of pins knocked down on the first ball of the following frame. Bowling scores accumulate each frame until 10 frames are completed. If, in the tenth frame, a bowler rolls a strike or a spare, they are allowed bonus balls to determine their score.
Once each player has finished the ten frames, the resulting highest score determines the winner.