TAKE IT SLOW!!!

I haven't fallen over yet *knock on wood* but what I do-

*practice clipping in/out/in/out/in/out until you can do so fairly reliably (i.e. w/o looking) and get a decent feel for the action. You can do this on a trainer, or... the hard way, with your seat lowered, leaning against a wall w/ your shoulder for balance, clipping in/out on the wall side. The latter is sorta dangerous, but if you don't have a trainer, it's my best suggestion.

Then take it outside to a nice, open place w/ long straightaways and generous bike lanes.
Clip in and out continuously as you ride. Get used to the feel. Also get used to the feeling of unclipping and pedaling for a little bit, just as you slow and stop, without being clipped in.

*Unclip long before you have to. Delay leads to a time crunch which can lead to a panic which can lead to overcorrecting and tipping over.

*Unclip with both feet just in case you tip your weight one way or the other when stopping. Not everyone does this... maybe I'm just 'special'...

*At first, clip back in once you've gotten good momentum. As you get more experienced, you may want to clip the foot that's still on a pedal at a stop, or leave it clipped in, and just park it with one foot. Do what feels right to you.

Above all, be careful and patient with yourself. Everyone has their own learning curve.
Hope this helps
There are other threads on this topic- just go to the 'search' and search for 'clipless'