The pre-glued hot melt tape works very well. Lay on the edge with a hot dry iron and move slowly, following with a wood block to continue to press down. Depending on where you buy it, it will be at least 13/16", possibly 7/8". If it's only available in certain lengths...like 8', you will pay too much. If you can, buy it on a continuous roll. I find the best way to trim the length edges is just with a mill file.
Lay the file on the plywood, and tip the front of the file up slightly, so there is a slight angle. Use the edge of the file in a push only stroke with the handle of the file leaning in the direction of your movement. IOW, you don't want to file into the grain, but rather you are rasping (breaking it off), with the edge of the file...on the the grain. I could show you in 5 seconds, but it's harder to describe. You'll get the hang of it pretty quick.
Using a trim router with a flush trim bit can catch the grain and tear it out, or, it could fold the veneer down. You can trim the ends with a combo square and a sharp utility knife, or use a flatbed paper cutter. To make a fairly invisible seam between two edges, they can be scarf cut. For butt edges, trim the mating edges at a slight angle so the veneer has a very thin edge meeting the other edge.
It shouldn't need any sanding other than just to clean it up from being handled (body oils and such). It will take stain and finish very well.