Make the outside
I chose two boxes, a wide one and a narrow one. I painted them, cut a square in each one to make a window, and attached the two boxes with Velcro. The back of the machine also closes with Velcro.
The capsules are released through a trap door in the narrow box. They eventually reach the prize door at the base of the wide box.
Don't forget to add a coin slot, and a door in the top of the narrow box to put the capsules in!
Make the inside
The capsules fall into a plastic tube (a plastic bottle with the ends cut off). They fall into a cup with a doorway cut in the bottom. Coins fall into another cup (the bottom of a plastic bottle) that is attached with Velcro so it is easy to remove.
Build the circuit
The circuit consists of Power + Wire + Slide Dimmer + Wire + Servo. A short popsicle stick with a hole drilled in it is fastened to the servo arm. A string tied through this hole lifts the trapdoor. Make sure to cut holes for the slide dimmer and the second wire.
Other things to keep in mind
This project required a lot of trial and error. I found that the trap door was too lightweight and would not fully close. Taping four coins to the back helped somewhat, but making the door itself out of heavier material may have been a better solution.
Also, because the plastic eggs are smaller at one end, they sometimes jammed inside the machine. I taped a marble into each half of each egg in an attempt to balance the weight. This helped a little, but round or cylinder shaped capsules may be a better choice for this kind of machine.