Fall down once, get up twice! How does that saying go?
Here's how we teach to clip + unclip in our Bike Skills clinics. It's pretty foolproof.
To clip in + start:
Straddle the top tube
Do not sit on the saddle
Hands on the hoods + apply brakes
Clip in at the BOTTOM of your pedal stroke (6:00) -- this gives you resistance.
Lift the clipped in pedal up to 11:00
Release the brakes and push off with the clipped in pedal, using your body weight to gain momentum
Look where you want to go. Do not look down at your feet.
Immediately lift yourself up onto the saddle.
Let your second foot find the pedal. Don't worry about clipping in until you have some speed (stability).
Pedal, pedal, pedal. Speed is your friend and you want to gain momentum as quickly as possible.
To stop and unclip:
Stand on the pedal that you WON'T be clipping out (this one tip will prevent you from leaning the wrong direction).
Do NOT look down at your feet -- look where you want to go.
Keep up your momentum until the last minute (stability).
Unclip at the TOP of your pedal stroke.
Apply the brakes, bring the bike to a stop and step down to straddle the top tube.
I used to believe (like many others) that you had to fall X number of times when learning to use clipless pedals. I no longer believe this. You don't have to fall. Speed is your friend (it keeps the bike upright) and your goal when starting is to gain momentum/speed as quickly as possible. Your goal when stopping is to maintain momentum/speed as long as possible before stopping.
Good luck!