I was taught to sharpen a drill by:
First, ensuring the wheel is running concentric to the grinder. On a bench grinder used by a variety of people this can be a challenge in itself. I keep a chunk of old wheel in my box to use as a dresser. Flat work face and square corners with as little runout at possible is a must. For some reason, holding the wheel rather than resting it works better for truing up the wheel, least it does for me. Never really understood this.
From there is a function of always keeping the tool moving and ensuring your parallel to the existing cutting surface. It takes very little pressure. I was taught to hold the drill in such a way that when inspecting the edge, have the light cast a shadow (indirect light) on the drill cutting surface. Look at only one side. If it looks longer than the other, rotate the drill 180 and look again. If the same side still appears longer then the drill is pretty dern close to being on center. It's tough to explain this and I hope I'm doing allright. With practice, meaning jobber drills often end up as screw machine length when starting out, it'll come to you.
A healthy human eye has about a .002" resolution. That being said trust your eye if your vision is decent/correctable. Staring at it too long is about the same as staring down the sights too long. Things tend to go hell quickly. "If it looks right, it is right" kinda' works for this.
Don't rest the tool against anything other than your hand. It'll chatter the finish 9/10 times. Your hands dampen this mysteriously enough. Especially on a bench grinder with a wigglin wheel.
Again, having the wheel properly dressed is the hardest part really.
Splitting the point is a bit more work. The edge of the wheel has to be very crisp in order to do it right. Just takes practice though.
Good luck.
C