I originally designed the pieces to be shot glasses but due to financial constraints I needed to shrink the size and use a different material.
I used Solid Edge ST4 for mine but the basic concepts and tools are pretty consistent between 3d modelers.
You will need:
Some form of 3d modeling software
and either a 3d printer of your own or use a site that does it for you (I used http://www.shapeways.com)
If you use the sire you will also need money to pay for it to be made.
You will also need a basic understanding of the modeling software you will use.
I will be referencing the tools I used for Solid Edge so the names will not always be the same for you but it should still be understandable as to what it does.
If anything is unclear or you would like more clarity or have any questions at all then please contact me and I will answer you as soon as I can and update my Instructable as needed.
Step 1: Reference
I found it helpful to actually place the image on my sketch plane so that, while I was making my outlines, I had my reference.
This is optional, if you want to design yours from scratch then go right ahead.
Step 2: Pawn
When you design this piece and all the others you start off with an outline of the basic shape.
Because the pawn is symmetrical only half of it needs to be outlined.
*When outlining keep in mind the tolerances required by the 3D printer. On Shapeways they have the requirements of each material so design with your material in mind.*
Then you will use the revolve command to create the final shape.
A lot of times it is required that your outline is a closed profile so just make a line down where the center of the revolve will be and select that as the axis of revolution for your revolve.(My axis of revolution is the small red dashed line.)
Your revolve will be a full 360 degrees around.
Although mine was originally designed as a shot glass yours does not need to be. However I will suggest that you make it hollow to cut down on the cost. This is easily achieved by using the offset command when making your outline. If the requirements for your material do not allow for a closed off hollow, you will need to make an opening. If you want to keep the look of your pieces solid then make the opening on the underside of your piece so it will not be seen when the piece is standing.
Step 3: Rook
You first need to outline the shape and then revolve it 360 degrees.
Now the rook has the added feature of the four indents in the top.
This is achieved by using two cutout commands on perpendicular planes.
Then use the round command on any sharp edges.
Step 4: Knight
However first you will still need to make an outline only it will need to be a full outline.
Next revolve the portion that makes up the base of the knight.
Then make a symmetrical extrude of the horse shaped portion to the extents of the round.
Now here is the hard part. From the top plane of the knight's head you will make a cutout shaped like the top of the knights head and remove the outside material down to the top of the revolved base.
Then you need to use the draft tool to put a slope between the base and the side of the horse shape. (This will take a bit of trial and error to get it to look the way you want)
Then round any sharp sides the knight has.
*If you need to make this one hollow I suggest using the thin wall command*
Step 5: Bishop
After you have revolved the basic shape you need to but in the slash.
Use the cutout command to remove all the material within the slash.
Then make an outline that is smaller then the original one and revolve that to fill in part of the slash.
Round the sharp edges.
Step 6: Queen
Step 7: King
After the first revolve create the cross shape and extrude it out in the four locations.
Then use a revolved cut to round the outside.
Then round all sharp edges.