I started by looking up pictures of R2D2, and quickly realized to do it correctly it really needed a custom stand. This is what I started with.
The frame is wood and cardboard with a PVC pipe running up the middle. The PVC is mainly structural support so the cake doesn't slide off the stand, but the choice for this size PVC wasn't completely random either
My wife was nice enough to bake six 9" round chocolate cakes for me. These were of the standard Pillsbury (or similar) variety.
Next came alternating layers of cake and butter-cream icing. The recipe for butter-cream is simple. I do it from memory, but I used something like the one found here with just butter and no shortening. http://www.wilton.com/recipe/Buttercream-Icing
This whole thing was topped with a cardboard ring to provide a crisp edge at the top. The outside was then frosted with a modestly thick layer to make a cylindrical shape.
The whole thing is covered with fondant. I make a marshmallow fondant myself to save time and money. http://www.wilton.com/recipe/Rolled-Marshmallow-Fondant
To make to top dome I added CMC powder to the marshmallow fondant. This turns the fondant into gum paste, and turns the fondant hard after it dries. This was then molded into the inside of a 9" semi-spherical bowl that was coated in vegetable spray and powdered sugar.
Rice crispy treats were used for the legs. I didn't document this beforehand but here is a posthumous picture of the leg from the inside.
This was all assembled and decorated with fondant and black decorative icing.
This gets me to the part that made this more than just a cake. the weekend before I was discussing the initial planning phase of this with some friends, and I joked that any R2D2 worth it's salt should be able to project Princess Leia. This quickly escalated into a review of the parts I had laying around and some test electronics. First I needed the video to project, which I found unsurprisingly on youtube.
Next I pulled out my raspberry pi and pico projector, but quickly abandoned the raspberry pi as it was having trouble playing the video. I landed on a netbook on the outside running VGA to the projector in the cake. The PVC selected allowed all the cables to fit up and through the cake to the outside. The setup looked like this.
For the finish touches I added a birthday message to the end of the Leia Message, and topped the cake with R2D2's head.
And a video showing the whole thing in action.