Use Bicycle Shoes for the First Time

Bicycle shoes and their pedals are a great way to go faster on a bike, but if used incorrectly, they can be dangerous.

Steps

Put on your shoes, as well as the pedals onto the bike.
Mount the bike like you would normally.
Clip one foot in, whichever you feel more comfortable with. You will hear a pop as your foot clips in.
Push off with that foot, then clip in your other foot.
Take a few pedals to gain some speed.
Try to un-clip by twisting your foot. If you can't, don't panic, just keep riding. Keep un-clipping and clipping in while riding so you can do it easily.
Come to a stop, put the foot down that is unclipped.
Unclip the other foot if you want to.
Keep practicing this.

As you gain experience, un-clip closer to the stopping point.
The first few times, un-clip way before you need to.
Learn to use the pedals to your advantage, by pulling up in the pedal stroke rather than just pushing down.
Eventually you will only un-clip one foot.
You can then clip in to one pedal while off your bike, push off, then swing your leg around and clip into the other pedal.
If you still can't get the hang of it, try toe clips, a cage like pedal that you put your shoes into.
Read up on your pedals to adjust float (how much you need to twist to un-clip), how hard you can pull up without it un-clipping, as well as keeping them working well.

Obviously, be careful. Get to know your shoes/pedals before you act like you have been using them for years.
If you come up to an intersection and cannot get unclipped, fall over correctly. Everyone has done it, so don't be embarrassed.