Thanks everyone for replying! Here are the things I learned:

1. I should try not to extend the hand out and not fall on the palm or shoulders. Hitting the elbow would be least damaging for the hand I guess.
2. I should try to fall in a way that probably the knee hits first, and then roll over gently on the back.
3. Keep calm and also yell OH CRAP at the same time
4. Practice unclipping a few feet before stopping (which I am doing now) and then slowly close the distance.

Guess I'd wear my biking shoes even during my everyday commute on uni campus until I get used to clipless. Hoping safe falls or no falls at all.

I just joined this forum and I am pleasantly surprised by how active this place is. Thanks again. I hope you guys enjoyed/ are enjoying the eclipse today (if you're in the US).