Before there were rotary blades people(my husband included) sharpened knives on a soap stone. My mom always sharpens hers on a crock.
I learned this aluminum foil trick a few years ago and it does work.
Basically you need some surface that will be abrasive against the metal blade(knife or rotary).
I have sharpened small scissors by cutting foil and it will work. It is not as efective as a store bought sharpener.
You can buy a rotary cutter sharpener and they work great!! I have used one and keep one on hand all the time. It really extends the life of your blades! And we do a lot of cutting!!!
I use Tri Sharp dual rotary blade sharpener. I got mine at Joann's and i saw they have them online. They are worth the investment!
You can also buy replacements for the circles that do the sharpening.
But if you don't want to spend the money the foil does work!