Originally Posted by DannoXYZ

Be sure to pick low gears and spin your legs fast. You shouldn't feel any resistance on the pedals, but rather that your legs are going to fly off from spinning. This puts the lowest loads on your knees and joints.

Although it really sounds like your cleats aren't set up properly on the shoes. In the old days with cage-pedals and cleats, we'd install the bolts loosely and let you ride around for a couple of days. Your feet would have a lot of room to move and they'd land in a position that's natural on the pedals. The pedal cage would make a line on the shoe over time. Then we'd align the slot on the cleat with the mark and tighten everything down. Depending upon the shoe+pedal system you have, this may or may not be a technique to use.