What size board should go under a twin trundle bed mattress?

If you are referring to something to serve as a foundation/box spring, you need (likely) a Twin bunkie board; which is a 2" version of a box spring. You likely have about 6-7" of space so after the board, you can possibly squeeze a Polypedic twin mattress or the cheaper 4" version. Both sold by Michigan Discount Mattress

• just ask for a Twin BUNKIE BOARD ... don't use a piece of plywood

like some people will advise you to do. Hope that's helpful.