Clip-less pedals bind the shoe to the pedal much like shoes bind to skis. There are many different types and it’s important to know what kind of pedal you use or plan to use before buying shoes. A common pedal is the ATB (All terrain bike) SPD compatible. This type of pedal can be used for both Mountain bikes and road bikes. Road pedals such as the “LOOK” type use a cleat instead of a clip and should only be used on road bikes.
Clip-less pedals improve cycling performance by correctly aligning the foot on the pedal and give the rider the ability to spin faster without slipping of the pedal. Furthermore, clip-less pedals allow the rider to apply power on the up and down stroke whereas regular pedals only give you power on the down stroke.
Buying cycling shoes can be very confusing to a new cyclist. Most shoes come in European sizes and every brand seem to fit differently. It’s best to visit your local bike shop for shoes but sometimes it's hard to resist the deals from Internet retailers. Before buying look for a sizing chart for the brand you intend to buy. Charts are usually available in the help section of the retailer's website. Also make sure the shoes are compatible with your pedals.
A generic shoe chart to give you a general idea of your correct shoe size: