When I first started, this is how it went.

Start on a level surface. Straddle the bike. Hold the bars still and clip in one foot while the pedal is near the ground (so it doesn't move when you push down). Doesn't matter which foot, everyone is different. Then lift that foot (with pedal now attached) to about 45 degrees forward of straight up and down. This all happens while standing still.

Then, gently push off with the foot on the ground WHILE pushing down on the raised pedal. This should give you plenty of speed to remain upright while cliping in the other foot. If not, just put the unclipped in foot on the pedal and pedal a few strokes to get going. When you are ready to clip in the other pedal, do it with the pedal in the up position (holding it there by keeping the already clipped in foot in the down position). Voila!

As you get more proficient at it, you'll get better and you'll learn more grace and the ability to do this 1) on the fly or 2) on an incline.