Ohhh! My mom used to decorate cakes all the time (or it seemed so). She was very, very talented.
Left over frosting always went on graham crackers. Either open faced or as a “sandwich.” Of course, you have to like graham crackers to enjoy it, but I remember it quite fondly and would love it even now.
Use a spoon. Scoop up and insert into mouth of any passersby. With three/sometimes four teens in the house, no frosting survives more than an hour or two.
Freeze - Unless it’s French buttercream with beaten egg, it will keep perfectly in the freezer forever.
Refrigerate for a long time
Bake another cake
Do the graham cracker thing, but build a pseudo-gingerbread house out of them, using the frosting as grout. Actually, that would be a waste of good frosting unless you actually eat the whole thing.
My mom froze leftover buttercream icing. I remember watching her make a chocolate cake and being amazed that she had this mish-mash of pink and green and yellow icing to which she added melted baker’s chocolate and – voila! – chocolate icing.
Put it into a sealed container in the refrigerator, where it will keep very nicely for weeks. Unless it calls out to you in the middle of the night, in which case you can whittle away at it a spoonful at a time.
Take two vanilla wafers. Spread frosting on flat side of one. Put flat side of other cookie against frosting. Eat. Repeat as needed. Or just spread a dab of frosting on the round side of each cookie.
You can crumble up cake into frosting, roll it into balls and dip it in/pour over a glaze like melted almond bark or melted chocolate. The recipes I’ve seen for that use cake mix and canned frosting, so I don’t know the proportions for homemade stuff.
A variation on graham crackers: sandwich some peanut butter between two graham crackers, then spread frosting on the tops. As I think back to my mother’s kitchen, those rare treats were even better than the cake, especially when the frosting was chocolate (which it always was).