First, choose a location for your bookcase and determine the size that best fits your needs. It may help to make a simple diagram of the bookcase you’re about to make, noting the dimensions for each part.
With your dimensions in hand, you are ready to cut the top, sides, and interior shelves out of 3/4” birch plywood. Since the birch plywood comes in 4’ x 8’ sheets, it will be easiest to use a table saw to rip down the lumber to your desired width. Don't concern yourself with cutting the lumber to the proper height (or length) yet. That will be done in the next step.
Use a miter saw to cut the top, side panels and interior shelves to the appropriate length. The miter saw will make a cleaner, more controlled cut than the table saw, and is a better choice for smaller pieces of lumber. If your dimensions are too large to be cut on a miter saw, use a table saw, but take great care to make the cuts as clean as possible.
The interior shelves need to be rabbet cut into the two side panels of the frame by using a router. Rabbeting the shelves into the frame will make the unit much stronger and allow the shelves to support more weight. In order to make sure you router these the rabbet grooves at the same position in both side panels, lay the two panels side by side on a table and screw a piece of scrap wood across both ends of the panels, effectively making them into one wide board. This will ensure that your lines are straight and even. Then, find the location of your first shelf and use a T-square to draw a 3/4” strip across both side panels at once. Draw another 3/4” strip at the location of every shelf you intend to put in the unit. A good rule is to space the shelves 16 inches (on center) apart.
After the grooves have been marked on the shelves, you will need to router them out, which will create the rabbit joints discussed in Step 4 (Image 1). To do this, clamp a level or straight edge along your newly marked shelf lines to use as a guide upon which to drive the router. A router is a very high velocity tool, and it can easily run away from you, so making this straight edge guide is essential to getting straight joints (Image 2).
Start by affixing the top to the two side panels using wood glue and finish nails (Image 1). Then, install the shelves by putting glue in the rabbet joints and sliding the shelves into the joints, one shelf at a time (Image 2). With the shelves in place, add finish nails through the outside of the unit to hold the shelves in place (Image 3). If you intend to hang the unit on the wall, you will want to glue and nail a 2” strip of wood across the back top edge to use as a cleat. Make sure this cleat is flush with the back surface so the bookcase will mount flush on the wall.
With the unit built, it’s time to finish it off by covering the rough plywood edges with nice finished piece of 1-1/4" poplar. Cut the poplar to the same dimensions as the exterior panels using the miter saw. The angles should be joined with 45-degree angle cuts for a smooth, tailored look. Use wood glue and nails to attach the finish framing to the bookcase (Image 1). For the faces of the shelves, you can get even more creative by using a 1”-wide decorative molding (Image 2).
Allow 24 hours for the wood glue to fully dry, and then sand it smooth and fill the nail holes with paintable or stainable wood putty. Use a tack cloth to wipe off any debris or sawdust created by sanding, and then paint or stain the unit to give it your desired look.