Before painting grout you want to get yourself a gallon of grout cleaner and clean and scrub the grout and tiles as well. It will deodorize and clean away grease, grime and stains. The grout will look brand-new again.
And if you visit a tile store or go online you can find grout colorant which is an epoxy latex. You can color the grout to the original color or you can choose any new color. You can even make a darker color a lighter one.