First off get a large box, put a piece of paper in it, put some drops of paint on the paper and then throw in a couple of acorns (tops removed).
Now is the fun part, let your child shake the box. Notice I have a box with high sides. I have done this before with lower sides and we have had acorns flying through the house with paint on them.
Another fun way to use the acorns is to get an old Pringles can, wipe it out and slip a piece of paper in the can.
Now add a few drops of paint and the acorns.
Tape the lid on good and hand it to you child to shake. It makes a great noise too with the metal bottom.
They can also use the acorn tops as stamps.