Using a Tape Measure
Set the ladder below and just to one side of the basketball rim.
Climb the ladder and lay a yardstick across the rim so that there's an obvious midpoint on the yardstick from one side of the rim to the other. The diameter of a rim is 18 inches, so you can, for example, set the 3-inch mark on the yardstick on one side of the rim and the 21-inch mark on the other. The distance between the two marks must be 18 inches to ensure that you're measuring the diameter correctly. The midpoint in this scenario would be the 12-inch mark, since it's 9 inches from both sides.
Measure the distance from the 12-inch mark on the underside of the yardstick to the ground using the tape measure and the help of your assistant. This will give you the exact height. Although it would seem possible to simply measure from one side of the rim, regulations state that the height must be measured at the center of the goal.
Using a Plumb Bob
Attach an 11-foot piece of string to a plumb bob.
Set the yardstick across the rim in the same manner as above.
Hold the unattached end of the string to the midpoint mark on the underside of the yardstick and drop the other end with the plumb bob. Pull the string up until the bottom of the plumb bob is just making contact with the ground.
Mark the point on the string where it touches the midpoint of the yardstick.
Measure the string from the mark you made to the end of the plumb bob to get the height of the rim.