Given that advice on building homemade arcades is fairly easy to find, I'll be focusing on how to make yours look good. So maybe this is more, "How to Keep Your Arcade Cabinet off of Crapmame." Or sort of a "Martha Stewart Gives Advice on Arcade Machines," which I totally wish she would.
Step 1: Applying Control Panel Artwork
Though not the most robust option, printed graphics behind acrylic panels will look brighter and just pop more. I don't know the physics behind it, but clear acrylic just makes stuff look better. Printed graphics are much cheaper than vinyl decals, and give you freedom to design with as many colors as you feel like.
Cover the whole panel in double-stick tape, and leave one side unsticky.
Next, line up the graphics. Holding it up to a light helps with this. Tack down the sides with low-tack tape to keep them aligned.
-Tip: make sure to leave enough bleed to run off the edges, and enough gutter to keep your graphics from getting cut off (or close to it).
Peel back the waxed paper from the double stick tape, and carefully lay down the graphics. Move from one edge to the other, smoothing down the artwork as you go.
Now trim the edges. Poke a blade through the middle of a hole, and cut to the edge. Keep the blade pressed against the edge as you work your way around the cut. The edges are cut the same way, but they're less curvy, so you can relax a little bit easier.