The easiest way is to bowl at a house that has a CATS or Qubica system haha. The crude way is to take a video of a shot and slow it down. Count the number of full revolutions from lay down to contact with the pins, and then mark down the exact time it took the ball to get down the lane, then you have a small sample size to multiply, the formula for which is

R=revs
S=seconds
RPM=revs per minute

(R/S)*60=RPM

So in an example, if you counted 15 revs in 3 seconds, you would take 15 (R) divided by 3 (S) to get your revs per second (5). Then you multiply 5 by 60 (seconds in a minute) to get 300 (RPM).