Say you need a 12" radius marked out. Take a nail, tap it in at the center of the arc, leave some of the nail sticking up. Tie a piece of string to the nail. Measure out 12" on the string, tie a pencil to the string, pull the string tight, and you can draw a curve that way.
You could also do the same thing with a ruler or yardstick if you don't mind poking holes in it.