For a perfect circular tree ring, loosely tie a string to the trunk about 12 inches off the ground, extend it out the desired distance and, keeping the string taught, walk around and mark your line.
You can also use the handle of the shovel as your ruler, laying it down, identifying the distance out on the handle and repeating around the tree. This works well if you cannot find any string.
Its important that the width of your tree ring is in direct proportion to the size of the trunk. Large trunks should not have small tree rings and vice versa, this simply looks silly. A good starting point is 10″ out around the tree for every inch of trunk size, (i.e. a 2 inch wide trunk should have a 20 inch tree ring).
Do not create a small tree ring around a large tree just to add mulch. Instead spray roundup, 4″-6″ out, around the base of the trunk, eliminating the grass and also the danger to the bark from mowers and weed eater damage.