i'm not sure what pedals they use at your gym. but let's see if i can explain what they use at mine.......
the pedals have toe clips(that your toes just slip into, and you wear regular shoes), and the metal lock in clips. the pedal has the female part of the clip. the bike shoes have the male part of the clip. however, most bike shoes don't come with the male part in the box. that is purchased separately, and are sold at mist bike shops. the male part of the clip screws into the sole of the shoe.
anyway.....i'm not trying to be a know-it-all. just sharing what i've experienced.