Drill 2 holes (brace and bit if you're being serious about "hand" tools) with a forstner bit (or hole saw), then connect them with a cut using a coping (or jig) saw. Chisel/file/sand as needed.
To expand a little... in order to help with tearout, drill from both sides by marking centers on each side and drilling halfway through each. Those look like 1" to 1-1/4" holes, if you're buying deliberately, but really, any old size should work well enough. (Bonus attribute if you're doing this with a hole saw is that the wooden plug is really easy to remove when there's half of it already sticking out of the hole saw.) Personally, I wouldn't use a spade bit, as they seem to tear a lot, which would require more cleanup.
The very attractive pictures were of fairly thick stock. If your project isn't quite as thick, I'd leave a bit more meat at the edge of the hole.
Everybody has a different preference for setup with the coping saw, but if you haven't tried it already, set it up to cut on the pull stroke. You might find you have better control and less blade deflection.
Cleanup on the inside would be easiest with a round or oval rasp, followed by something a bit finer. (You could also rough it with a sharp chisel or gouge.) After roughing, transition to sandpaper. If you roll the sandpaper into a cigarette sized roll, it'll hold shape fairly well and be able to knock down the edge to perfection.