I'll nth the advice of practice in the parking lot.

Push off, clip in, pedal, clip out, stop. Repeat.

Practice with both legs.

One advantage of clipless pedals is that it is easier to pedal with one leg. Practice that, too. Useful skill if you break a crank arm and still need to get home.

Every one falls. Even experienced riders. I practiced in a parking lot doing slow laps around the truck. Lap and stop and unclip, lap and stop and unclip.....did not fall until I was in a parking lot at the HHH in front of about 100 people. We all laughed.

I echo the suggestion of practice--but not in a parking lot first. Practice clipping in and out while supporting yourself on the bike against a wall or in a doorway. Do a couple of sessions of practice, 50 to 100 times clipping and unclipping. Practice with both feet. It will get much easier.

No, not everyone falls. Y'all need to stop saying that and scaring folks!
Riding SPD since sometime in the '90's and they haven't contributed to any falls. No toe clip-related falls prior to that.

I'm sure some clipless falls happen partly because the cyclist has been convinced that they are doomed to fall. Self-fulfilling prophecy - Wikipedia, the free encyclopedia

Would practicing on a spinning bike help? I have access at my gym and use them during the winter.

My answer to practicing on a spinning bike is YES... in fact that is how the bike shop had me practice before the 'turned me loose' with the shoes... it was my first purchase and they wanted to be a good shop and help in any way possible.