You need: 1 large dish/tea towel and a long piece of sturdy ribbon that won't fray easily (I used about 2 yards - measure the ribbon right on your kid, as it needs to be long enough to go around their neck, down their sides and tie in the back
Hold the towel up to your kid, centering it on their chest and holding it at about the level it should sit when finished. Use a pin to mark about an inch in from their armpit, and another to mark their waist level (if you mark a bit lower than their current waist area, the apron should still fit as they get a bit taller!).
Fold the towel in half, lengthwise, and using a rotary cutter (or scissors), cut from pin to pin, making a curved cut (don't worry - you'll be able to eye ball it, but if you're totally chicken, draw the line or use pins to mark where you want to cut):
When you open it out, it'll look like this (see? it already looks like an apron!):
If you're feeling particularly tricky (and the back of the dishtowel isn't ugly), you can fold up the towel from the bottom and sew up the edges to make a pocket. Then sew straight vertical lines from the fold to the top of the pocket to make smaller pockets:
Lucky for you, these only cost a buck or two, and a minimal time investment, so you'll feel just fine about your kids totally yucking them up! You can throw them right in the washer, or you can make more!