Practice, practice, and practice.
To hold the drill for the relatively long holes these require, do you
hold the hand drill with your index finger parallel to the axis of the
drill, and middle finger handling the power trigger? This allows more
control over the drill as it lowers the center of gravity of the drill with
respect to your wrist, and brings it closer to being along the center
line of your forearm.
Use a set square (or fixed shop made fixture) to mark out the center
line of the board that houses the bulk of the screw. In the case of
the sheet stock you mentioned, you would set it to 3/8".
Think thrice, measure twice and cut once.
Sanding is like paying taxes ... everyone has to do it, but it is
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