"Sticky Paper", as I call it, is simply contact paper. Tape it, sticky side out, to the table, or for real entertainment, to the wall. Give your little one cut up colored tissue paper, feathers, cut up greeting cards, construction paper, qtips, cotton balls, pretty much any lightweight material you can think of, and show them how to stick them to the paper!
We made a piece of St. Patty's Day themed sticky paper art.
If you put an equal sized piece of sticky paper on top (sticky sides together), you have a lovely piece of "stained glass art." If you're feeling super energetic or crafty, you can put the outline of a shape in construction paper, then trim around the shape. That way, when your little one is done, you have a cute piece of themed art (for instance, if I weren't a suck at home mom, I could have made today's art in the shape of a shamrock. Since I didn't, I'll mention the benefits of letting your child be creative instead of making them restrict their artistic talent inside a pre-determined shape!)