Send your kindergartners on a scavenger hunt for various shapes, giving them a list of items such as "a green triangle" or "a gold star." Let them look around the room or take them on field trip with several supervisors. You also can show them a short movie and ask them to write down all the shapes they see, or you can give them a series of pictures and ask them to identify the shapes in each one. Have the children attempt to replicate a picture by drawing the basic shapes they see in it.
Set up a game with two-dimensional shapes cut out of construction paper and various objects that have the same shape. Ask your kindergartners to match the cutouts to the objects with the same shape. You also can set up a similar project using drawings, asking kindergartners to draw a line matching shapes in column A to shapes in column B, or you can ask students to match cutout shapes of different colors. For a little variety, you can play Bingo with shapes, asking children to draw nine shapes with different colors on a card and either showing kindergartners the shape they can mark on their cards or saying the name of the shape. You don't necessarily have to use basic shapes -- you can use more complicated shapes like animals or household objects as well.
Show students cutouts of various shapes and see how fast they can say the names of the shapes. Then show them flat objects and ask them to draw the shape as well as name it. Finally, ask students to cut out shapes of their own according to the type of shape that you name. Ask them to try to cut out at least five different versions of a shape -- some big, some small, some different colors, some with different angles. Cut these shapes into puzzle pieces, and ask the students to try to put them back together, or even create new shapes.
You can use shapes to teach kindergartners about more than just geometry. Use shapes to teach kindergartners about colors by asking them to find shapes with certain colors or match different shapes with the same color. Teach kindergartners about counting by using the sides of different shapes as a visualization, or ask students to make shapes with a certain number of sides. Do jigsaw puzzles to teach them problem solving and critical thinking, have students or groups of students play charades with shapes, ask them to write stories about shapes, have students use different shapes as currency in pretend stores or use different shapes to play games that teach children about diversity, such as having students discover how many more objects they can make when shapes work together.