Test each of the heating elements with a multimeter to determine which element is broken if there is no visible broken wire. Touch a probe to each end. A broken element will read has having very high resistance.
Remove the broken heating element by unscrewing the ends of the element with a screwdriver. Depending on the type of toaster element, it may be held into place with rivets. Remove the rivets and remove the defective element.
Insert the replacement heating element where you just removed the broken element. Make sure the replacement element is the same structure, material and heat rating as the old element. Secure it into place with new rivets or screw it into place with a screwdriver. Again, the method of securing the element into place depends on the type of toaster oven.