One at a time, I let them share their shape with the class. They tell us the name of the shape and how many faces, edges, and vertices it has. I always let them throw in a little something about their object too. Then, students place their object on a nearby table into the correct shape category.
We always play a fun "Guess the Shape" game, too! I stuff solid shapes into a bag full of stuffing (tissue paper, paper shreds, etc.), and call students up one at a time, blindfolded, to pull out a shape and guess what it is by only feeling it. It's a great review game and actually goes very quickly.
We also use our table full of sorted shapes to tally and graph. If you'd like you are welcome to download this free Shape Share Day Tally Table for the ActivBoard.
We also make solid shapes during the unit before Shape Share Day. We always use these to have hands-on access to counting faces, edges, and vertices. Above, we taped them to a sentence strip and wrote each shape's name, along with how many faces, edges, and vertices it had. In the picture above, I had die-cut shape nets, but if you don't have those, you can download this free shape net page (featuring cube, pyramid, rectangular prism, and cylinder):
What fun things do you do when teaching shapes?