1. Make a rectangle with a width about twice as long as the height. Use a white fill and a light grey color for the stroke.
2. To turn your rectangle in to a grid, select it, go to 'Object > Path > Split to Grid' and change the settings circled in red. Making the 'Gutter' 0 will remove all space between sections of the grid.
3. The resulting grid will look like this. Each section of the grid will have the same stroke and fill properties as the original rectangle:
4. Select the 'Live Paint Bucket' tool and click on your grid.
Using a grey fill and no stroke, click on each section of the grid to make a checkered pattern. Each section will turn red when you hover over it.
5. Now select the Free Transform tool, grab the bottom left corner handle, start dragging it to the left, and then hold Alt+Ctrl+Shift and drag the handle over to the left further. It should now appear as if you are looking down at the grid as shown: (note: my image is reduced by 50% in this step)
6. Grab the top center handle and drag down to make the grid a about half as tall (mine is still at 50% size).
7. Now you will make a pawn chess piece. Turn on the grid by going to 'View > Show Grid'. Now zoom in to whatever size you're comfortable working with (I used 300%). To quickly zoom, hold Ctrl and press the plus symbol a few times. Ctrl and the minus symbol will zoom back out. Using the Rounded Rectangle tool, draw a round rectangle, using the grid to line it up.
8. With the Direct Selection tool, drag a selection rectangle around the two bottom points of the rounded rectangle, then hit 'Delete'.
And get the result shown:
9. Draw a rectangle and a circle to complete the pawn shape (to draw a perfect circle, hold shift while drawing with the Ellipse Tool). Use the grid to make it all symmetrical.
10. Draw a rectangle that covers up the right side of your pawn. I used a darker grey so it is easier to see. Now drag a selection rectangle around everything (using Path Selection tool), then open up your Pathfinder window (go to 'Window > Pathfinders') and click the Crop pathfinder.
11. You should now have a half pawn shape
Make a copy of the half pawn shape and move it out of the way (select everything, then Ctrl+C to copy, Ctrl+V to paste). You will use this later to make a king chess piece.
12. Select all of the objects that make up the original pawn shape (with Path Selection tool) and go to 'Effect > 3D > Revolve' The settings shown are the default settings. If yours are different, make the appropriate adjustments.
13. And the 3D pawn is born:
14. Now go to your copy of the pawn shape. Using the Direct Selection tool, click on the outline of the top circle (see image below). If you click right on the outline, it should appear as shown:
15. While still using your Direct Selection tool, click the right point of the circle. Now press the up arrow a few times until you have the result shown:
16. Now do a 'Effect > 3D > Revolve' again, just like you did before.
17. Draw two rectangles to make a small cross.
18. Select both rectangles, and click on the 'Add to Shape Area' pathfinder. This will combine them in to a cross shape.
19. Select your cross shape, and go to 'Effect > 3D > Extrude & Bevel'. The only setting you need to change is 'Extrude Depth'. Make it 10pt.
20. Move your new 3d cross on top of the king piece. Select the cross and the king piece and go to 'Object > Group' to combine them. As far as I know, you can not use a pathfinder to combine the two objects, because it will remove the 3D effects.
21. Place the pawn and king pieces on the middle area of the chess board.
22. Now adjust the size of the pieces and the chess board to your liking. Remove the grid ('View > Hide Grid') and you're done.
