Horses are measured in hands. Each hand is four inches. If your horse is 15.1 hands, he is 61 inches tall.
You measure using either a measuring tape or a measuring cane.
I prefer a measuring cane. They usually come with a level, and you can really get an exact measurement. I was unable to find a picture of a measuring cane.
It just looks like a regular cane with a piece of metal (ruler) that slides out from inside the cane. There is one more attachment on that, and that is what you put up to his wither to take the measurement.
You measure from the bottom of his front hoof (the ground) to the top of his wither. That's all there is to it!