To obtain the digital root of a given number, add the digits of said number. If the resultant digital sum has more than one digit itself, add the digits of the digital sum. Repeat this process until a single-digit digital sum is obtained. This single-digit sum is the digital root.
The number of times one must step through this additive process to obtain a digital root for a given number n is known as the additive persistence of n.
Example:
To obtain the digital root of the number 19843, add 1+9+8+4+3 = 25. Then add 2+5 = 7. The digital root is 7 and the additive persistence is 2.
Interestingly, if the digital root of a number is divisible by three, the number itself is divisible by three. For a more in-depth explanation of this divisibility rule, see 3.