Before worrying about mounting the engine, first flip the bicycle upside down and remove the rear wheel. This is going to be your powered wheel. The kit should include a plastic drive ring, which is a grooved, plastic circle about half the circumference of the wheel. Snap it into place on the spokes of the rear wheel. Thread the drive belt around the ring and put the rear wheel back on the bicycle frame, but don’t tighten it yet.
Attach the mounting brackets to the engine with bolts. The other ends of the brackets should attach to the rear axle. All the necessary hardware will be included in the kit. Now you can tighten the axle nuts and flip the bicycle upright. The engine rests on a mounting strap, which is bolted to the bicycle frame beneath the seat and resembles a rear fender. Loop the drive belt over the engine drive device and the idler pulleys. Slip the engine cover into place over the drive mechanism (it’ll help keep out water and dust) and tighten it.
The engine is now mounted, but you need a means by which to easily control it when your hands are on the handlebars. The kit should come with a kill switch and throttle lever. Each can be easily mounted on the handlebars with spring clips that allow you to reposition them while riding, if necessary. Cables connect the switches to the motor at the rear of the bicycle. Thread them along the frame, taking care that they won’t interfere with pedaling. Small clips or tie-down straps work well. Most kits call for the kill switch to be mounted on your left and the throttle on the right. Test the operation of each to make sure they operate smoothly with no kinking.
Variations on how to mount a motor on a bicycle exist, but, ultimately, it all comes down to figuring out a way to translate the turning motion of the engine drive into torque on the rear wheel of the bicycle to achieve forward motion with no human assistance. The more mechanically inclined out there could probably figure out how to adapt almost any small engine (like from a Weedeater) with the same result.