Assembly is pretty straight forward. A lot of soldering, but what did you expect. I'm not going to instruct you how to solder here. If you don't know check out the many instructables in how to solder.
After assembling all the boards you're going to want to figure out what you eventually want to do with it. This way you can add appropriate lengths of wires for the pots and tilt switches. As you can see from the image, my enclosure required decently long wires to place the pots and tilt switches in the appropriate location.
A note on tilt switch placement:
you need to figure out a location for your tilt switches that best fit your use. For me, I wanted to be able to use the device while it is laying on a flat surface and while being held vertically, about perpendicular to the ground. To that end, I placed once switch on the side of the enclosure with the leads pointed up so that when the device is laying on a flat surface that switch is always open and the screen will never clear. The other switch I placed on the bottom (the red part your seeing in the image above) with the leads pointed towards the top, that way when the device is held vertically the switch will be open.
For assembling the MIntyBoost I refer you to http://www.instructables.com/id/MintyBoost!---Small-battery-powered-USB-charger/
While we're on the topic you may be curious as to why I'm using a MintyBoost to supply the power to the project. I answer is quite simply that the MintyBoost is a nifty little device to step-up voltage. I designed the device to run off 5V and for the longest time I was planning on just using a 5V power supply that plus into a wall. I really didn't like that idea because I didn't think the LED Etch-a-Sketch would be much fun if it had to be plugged into a wall all the time. I looked some other step-up converters but didn't find any that would be able to supply the current I needed. Then I came across the MintyBoost. It can give me 5V and high current, it's small, and one less thing I had to worry about designing and building.