I'd intentionally made it oversize, intending to trim it flush. Trimming is a little more complicated than usual, because I needed to trim it flush on two faces. The end face extended a good 3/8", so I cut off most of the excess with a circular saw and the edge guide, then flipped the edge guide upside down to make a stable platform for the router. Aside from the use of the edge guide, flush trimming the edge face was unremarkable.
Once you have all the clamps on, take off the scraps of hardboard. You can clean up the glue squeezeout with a damp rag.. When the glue is dry, trim down the strip flush with the panel using a router and a flush-trim bit. Then cut off the ends of the strip with a flush-cut saw, and clean up with a block plane, an edge scraper, or a sanding block. Leaving the ends in place while you route the edge helps support the router.

So drill the benchdog holes through the MDF layer. Begin by laying out their positions. You'll want these to be precise, so that the distances between the holes are consistent. The vises you are using will constrain your benchdog spacing. My front vise worked most naturally with two rows of holes four inches apart, my end vise with two pairs of rows, with four inches between the rows and eight inches between the pairs. Because of this, I decided on a 4" by 4" pattern.
Next is the shelf. Start with the 24x48" piece of MDF. Clamp this on top of the base, and pencil in the outside of the stretchers and the inside angle of the legs. Flip it over, pull out your trusty cutting guide, and cut it to width and to length. Cutting out the angles is simple, with a jig saw. It's not much work with a hand saw. If you took enough care with supporting blocks and stops, you could probably do it with a circular saw. Since I did have a jig saw, I used it.
A woodworker's workbench isn't a table, it's a work-holding system. It's not something you set things on top of, it's a tool that holds your work. Where a worktable might have a machinist's vise bolted to its top, a woodworker's bench is built to accommodate a number of different workholding mechanisms, such as bench dogs, planing stops, hold fasts, or board jacks, and will usually have one more woodworker's vises integrated into its structure.
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Put the countertop on the base, put the MDF on top of the countertop, and line up the marks you drew on each end of the MDF with the countertop below it. When you have it lined up, clamp things down, and route the edge of the MDF using a 1-1/2" or longer flush-trim bit, with the depth adjusted so the bearing rides on the countertop. I clamped a couple of scraps of doubled MDF at each end to give the router base something extra to ride on at the ends.
With the inner jaw fastened to the bench, I used the router to flush-trim the jaw to the benchtop, across the top and down the sides adjacent to the top (stopping short of the discontinuity between the top and the legs). I'd thought this would be the best way to match up the jaw against the top, but I'd not do it this way again. It was very difficult to hold the router tight against the face of the jaw, and the result was a surface that wasn't as even as I had hoped.
The book is well written and easy to read. The illustrations, I'm sure were excellent in 1914 and, are still adequite now. Most of the designs seemed repetitive, though. I wish more attention had been given to lashing materials. If you are looking for that you will find almost none here. The book was fun to read and provided enough inspiration to make my brother and me attempt a large hut.