Well, laser cutting is a hall different story...
First you need to chose the material you want to use (wood, paiper, perspect), then measure the thickens of it. To be accurate you should make a ruler (scale) with a variety of measures. Lets say your matirial is 3.00mm thick then the range of your ruler needs to be from 2.8mm to 3.2mm in difference of 0.01mm.
(I used Rhino but you can use a variety of sketch programs).
After you design your scale, go to the machine and focus it Upload the file to the machine , origin it and test the frame that you have enough material on the machine, then cut it. After you cut it , you should test it (to find the best fit for the parts).
Now you sketch the parts of the game you want to make. I made a building game.
Make one piece and then insert the length of the cut and the thickness that you found most accurate.
now just copy and paste the number of pisses you want.
There are endless possibilities that you can choose.
Now we start cutting. You plaice the material you choose on the cutting surface and focus the lesser once again just to be shore.
After that you loud your files to the lesser cutting machine and do the same proses that you did with the scale.
After its finished collect the pieces and start building. Now that you understand how to create the pieces you can play with the design.
You can download the game file.
I also tried to make something more complicated...
**A small tip: you can use 123D MAKE to make your life a lot easier.**