I just went clipless about 2 weeks ago. I didn't have any problems at all and never fell.I love them.
I just get on my bike and start pedaling like I did without the clipless pedals. As I'm pedaling along, paying attention to the road, I wiggle my feet around until it feels like they're in the right place then push down and clip in.
The the first time I did it, I got a mile down the road before my first foot clipped in and then it was another 4 miles before I got the other one clipped in. The key, for me, was to just ride at a relaxed pace and pay attention to riding, occasionally calmly messing around with clipping in but telling myself "it doesn't matter if I never get clipped in, I'll just keep riding." Of course, now I have both feet in before I even get out of the driveway.
As far as the benefits - I didn't see a huge increase in speed immediately but pedaling differently is training different muscles. Now that those muscles are getting stronger, I'm getting faster. Before, I really only felt my quads being worked. Now I'm also feeling it in my glutes, calves, shins (I never knew I could work out my shin muscles before!), the fronts of my ankles (I can see new muscles there), and my lower abs. I am thrilled to feel it in my abs because I detest doing crunches.
On some of the long gradual hills, I like to play around pedaling with different muscles. First I concentrate on kicking forward for like 50 strokes, then on pushing down, then on sweeping back, then on pulling up, then on perfect circles. It makes the ride more interesting.
I'm getting stronger and faster and it's easier to get my heart rate up.