I am trying to put Skittles candy on the sides of a cake I iced with buttercream and they will just NOT stick! What can I do?

You should be able to stick them on with more buttercream as glue. I have never had this method fail me unless the object is too heavy, skittles shouldn't be too heavy though.

You could try Royal Icing.

Bite the backs off...

Srsly, a bit of tylose in a bit of water, piping gel, or gumpaste. Or the BC on the back but let it get partly dry, then stick on.

But first I'd just put a wet finger on the backs to soften them and see if that works. There is WAX on those things.

If not, there is always that bite....