Hi there!
I don't know anybody who hasn't fallen a time or two with clipless pedals.
I started with SPD and now am a converted Speedplay girl. I love the side to side foot movement I have, it's much kinder on my knees. I have big giant feet so I hated using cages.

I tell my new riders two things when they make the switch to clipless.

1) Pick a leg that is your clip out leg and remember to always LEAN in that direction.
2) If you even think that you might want to go near your brakes, clip out.

Of course there's always gonna be moments where for whatever reason you're gonna fall over. My last time was standing STILL, giving a pep talk to some newbies, I was standing up with my left foot on the ground and for some ungodly reason shifted my weight slightly and ended up falling over right onto a curb. OUCH....I claimed there must have been an earthquake but nobody bought it. Just call me GRACE.

I'll take those occassional falls for the increased power and pedal efficiency I get from being clipped in!!