There are basically three types of pedals: pedals with clips and straps, ``clipless'' pedals that a cleat on the shoe clicks into, and pedals with neither.
Clips work best if they are made of plastic and have two prongs that the strap threads through, to prevent them from bending sideways. The strap should be twisted one full revolution inside the pedal to keep it from shifting. The lock at the strap end should be near the outer clip end, such that the other end of the strap points up, where it is easy to grab and tighten when riding. Tightening is unfortunately necessary frequently. It is also often necessary to untighten the strap manually before removing the shoe, especially if the shoe has a cleat with a horizontal groove that fits into the rear pedal edge. This, imho, makes clips dangerous because you may not get out in time in an accident.
Clipless pedals come in a variety of shapes. The two most popular ones are Time and Look, which require a large cleat that makes it hard to walk with the shoe, and Shimano SPD and Ritchey, whose cleats are recessed in the shoe to make it possible to walk normally. There are various clones and other more exotic systems. Racers prefer Time/Look because they hold the shoe more tightly while Shimanos seem to get more float and play (they call it ``freedom'') with every new generation.
Clipless pedals have two advantages that make them useful for anyone except the most casual riders:
* They allow applying force during the entire pedal cycle, especially while the pedal is moving up. You will develop an entire new set of muscles that help you pull up the pedal while you push down the other (learning this takes concentration on pulling; pushing works by itself). This improves speed and acceleration significantly. It takes some practice to also push or pull the pedal while it is at the top or bottom point of the cycle. The purpose of the exercise is a ``round'' pedaling cycle, which reduces knee stress, makes it possible to climb steeper hills, ride in tight groups, and generally improve performance.
* They also keep the rider in contact with the bicycle. Losing contact with the pedals when hitting a pothole or other obstacles, or when riding fast over cobblestones can easily cause a crash. If there is a crash, the pedals disengage practically automatically. There is virtually no danger of being hurt because the pedals fail to disengage. (Clips with tightened straps, on the other hand, can twist the ankle in nasty ways in a crash.) I have crashed several times in many different ways and never had a problem.
Personally, I prefer the Shimano/Ritchey system simply because I have clipless pedals on all my six bicycles and never ride without cleated shoes. Riding to a grocery store and amusing the audience by helplessly staggering about like a penguin because of the cleats is not my idea of convenience. If I raced competitively I would probably feel differently about this. Shimano sells racing cleats that solve much of the excessive sideways play problem.
Shimano pedals can wear out in two ways: the little nose under the front part of the cleat can be worn down, which makes it very hard to disengage from the pedal. This is dangerous but rare. More commonly the front U-shaped back-facing grip of the pedal gets worn from its U shape to a soft curve, which makes the pedal disengage unintentionally. In this case you can either replace the worn part, if you can manage to unscrew it after years of use, or buy new pedals.
See also an article on " Shoes"