How do I clean shoelaces?

The easiest way is to put them in the clothes washer.  To prevent damage to the laces you can put them in a mesh bag which will somewhat protect them from machinery (as you can do with anything including delicate items like children’s stuffed animals).

For disinfecting you can soak them in bleach for 5-10 minutes or vinegar for 60 minutes before washing.  However note, if you choose to soak them in bleach you should wash them seperately from colored items (or include them in your whites cycle in case any of the bleach bleeds onto the other clothing items).