The basic idea is a radius on the leading edge of the tip and a square trailing edge and the whole thing is brought to a fine edge along the tip.
As I understand it:
The wind tries to run around the end of the blade due to the pressure difference between the front and back sides. Eventually it succeeds (creating a "tip vortex" of spinning air).
If it succeeds near the blade tip (the center of the tip vortex is near the tip) it reduces the pressure difference between the front and back near the tip, and thus depowers the end of the blade. This is bad. The end of the blade represents a LOT of your swept area, so depowering it costs you a bunch of output. Also: the wind making the turn and being deflected by the backside turns some of that lost power into noise.
Letting the tip be round makes it easy for the wind to run around it.
Making the tip sharp causes the wind leaving the front side to be jetted off for a distance before it can turn around. (The tip vortex is pushed out a bit.) By the time it gets turned around the blade is gone. So the pressure difference is maintained and the tip vortex spins away merrily downwind. That's why you want the end sharp. (This can be interpreted as virtually making the blade longer: Not only does the end remain powered, but the tip vortex's interaction with the incoming air can actually collect power from the flow a small distance beyond the end of the blade, increasing the effective swept area further.)
Rounding the corner makes the transition from the leading edge smooth. Discontinuities create vortex peel, drag, and noise.
(The leading edge is rounded so it splits the air cleanly, leaving the airflow attached to both the front and the back of the blade, at a range of angles-of-attack. Sharp would be somewhat more efficient - but only for a particular angle of attack. The blade would stall at other angles, with the airflow detaching from one side or ther other, losing far more than was gained. The trailing edge, on the other hand, is sharp so the two attached airflows reconnect cleanly, going in the desired direction, without creating a vacuum behind the join that would drag on the blade.)
I'm not sure about the significance of the angle between the flat portion of the sharp edge of the tip and the radius of the blade - whether it's better to have the trailing end farther out, closer in, or at right angles to the radius. I presume you want it to end just before it would be caught by the returning air from the tip vortex. I note that Sandia designed it to be about three degrees off from a right angle with the radius, farther out at the trailing edge, so the sharp edges of the tip and the blade's trailing edge made a sharp 87 degree corner. (They also started the sharp part of the tip within the rounded front corner, a bit behind the 45 degree point, rather than where the corner rounding transitioned to the straight part of the edge. And they curved the sharp edge in the upwind-downwind direction to track the midline of the airfoil shape.)