The first question you'll need to ask yourself when building a retro arcade cabinet is a pretty dangerous one: Which Raspberry Pi should I get? Resist the urge. The better place to start is to determine what you want the thing to play.
If it's a cabinet for Pac-Man, Galaga and other early arcade games, it can have a much simpler control panel than one would expect to have for Street Fighter, four-player beat-'em-ups or Golden Tee. Some fighting games require six action buttons for each player, while other arcade games rely on a trackball, spinner or other special control. Player numbers are also a factor, especially if a neat two-player panel begins to turn into a four-player panel.
Mocking up the controls on cardboard before drilling into wood is a cheap safeguard. A popular Raspberry Pi cabinet build shared on Maker Forums was similar, with the layout of the control panel tested out before the final material was used.
From there, there are three general paths for the cabinet itself: Make one out of plywood or MDF, purchase a flat-pack cabinet or repurpose an existing cabinet. Electronics can be quite tiny, but the furniture surrounding them is where the project starts getting ideas above its station.