Cutting the stretchers themselves is easy, although there's a lesson in getting the end joints to mesh with the end pieces. It's always better to adjust tenon size to fit mating mortises rather than cutting parts to the correct-on-paper size in the plans. If your mortises are wider or narrower than the specs (and they might be), then adjust your tenon dimensions to suit. You just want a gap-free fit, and identical distance between tenons on both stretchers.
With the stretchers fitting properly into both end pieces, it's time to think about the wedges that hold it all together. Success here depends on wedge location. Start by pulling the shelf ends and stretchers together with clamps, then mark the best place for the wedge holes you need to prepare on the tenoned ends of the stretchers. Be sure to extend hole locations slightly past the place where the outer faces of the ends will be. Take a look at the plan for details. This feature is small, but it ensures that the wedges pull all parts together tightly during final assembly.
Drill the bulk of the waste wood out of the wedge hole areas you've marked, then square up the holes with a chisel.
Make four wedges by cutting square sections of wood to 3/8" x 3/8" x 1", then taper them with a chisel, plane or sander to get the right shape. Adjust their size if the fit is too tight or too loose. Slightly round all of the edges of the project with a fine file or sandpaper, and do any finish-sanding required. Go easy on any power sanding; don't change the tenon thickness.
I typically don't bother with glue on these shelves, as the wedges hold everything together nicely. And there's no risk of glue stains on the wood.
I suggest you apply a stain or dye, let it dry, then finish with wipe-on polyurethane. It's durable, easy to apply and will make your project look great.
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