About a year and a half ago I made a stool from a piece of oak, with alder legs. I had just been given a new drawknife for Christmas and wanted to test it out by shaping some pole lengths.
The seat of the stool was shaped from a tangential section of a large log. First the log was split down the middle using a splitting maul, then the backside of the log was taken off with a chainsaw, ripping down the grain of the wood, which is slow-going compared to cutting across the grain. Using a tangential section meant that there was some lovely colour difference between the dark heartwood and the pale sapwood.
I drilled four holes with a brace-and-bit drill and an auger through the seat, to fit the legs. I shaped the alder legs with the drawknife into octagonal shapes, purposely leaving some bits of bark on the corners, which I think adds a nice effect.
To fit the legs into the seat I shaped the top of the legs down to pegs which could then be tapped into the holes in the seat, and finally wedged with thin slivers of hard yew. I made sure the seat was wet and the legs were dry, so the seat would tighten around the legs.
To make the pegs I sawed into the legs then used a flat chisel to split off the wood up to the saw cut, bit by bit. To fine tune I used the chisel to shave down the pegs.
Clearly I cut too deep on one of the saw cuts for the pegs, because recently the leg snapped off.
Instead of shaping new legs I decided to shape a new peg for the broken leg, and just have a shorter stool. I actually think the shorter legs look better, as one of the legs was previously quite bowed and looked a bit silly.