Paul HAS used fixings. You can just make out one of the two screws in the top of the block. If you want a cleaner look, simply plug the screw-holes with a dowel and chisel/plane it flush. The toggle has a screw in the centre too. These are utility pieces for storing tools. Concealed fixings are best reserved for the things you make with the tools.
For the main block: Find a block of wood which is about 5mm deeper than your handle. Sketch around the inside of your handle. Using a Coping Saw, cut out the profile of the inside of your handle. Slice that extra 5mm you allowed for from the top of your block to get your rotating toggle with matching profile. Fix the block with glue and two screws. Secure the toggle with a screw in the centre, leaving it loose enough so it rotates. Align the toggle to insert/remove your saw. Turn toggle 90-degrees to friction-lock it.
For the toe: Make a flat/low ‘bridge’ with just enough clearance beneath for the saw-plate to slide into. Or cut a channel/groove into a narrow strip of wood and slide the saw’s teeth into that. Some use a small triangle to support the saw’s front corner. Slide the saw in, toe-first, then lower the handle onto the main block, turn the toggle.
For shorter saws, you don’t need anything at the toe. The main block is enough to support the whole saw.