Dip the bar of soap in warm water, rub on to cap, rinse off. It will come up sparkling white, be careful not to get any soap residue on to your cap tally though. (Good idea to remove the cap tally when cleaning to avoid this.)
Always used a nail scrubbing brush and normal soap. Top it off we used white shoe whitner stuff, but make sure it's good water proof stuff and that it dries before the rain! Keep it clean, I brough a shower cap and placed my cap in there until I wore it.