First I cut off a piece of the end, by sawing around with a serrated flake and breaking it. A very easy task with such a pithy material.
After measuring the depth of the slot I want the bit to sit in I drill a small hole on that point on opposite sides of the shaft. You can easily use a flake for this task.
Some shallow grooves are made on the width you need. Use an antler wedge to split out the wood in between. Carve out as much as needed of the pith and edges with a flake.
Seperate a strand or two of sinew from a backstrap (or leg tendon) and wet them in your mouth to moisten them. Make sure the point sits in the slot such that the shaft will not wobble when spun.
Wrap the wet sinew around the point and shaft to securely haft it. When it has dried up you can snap off the ends of the sinew with a flake.