Stationary bike "clicks" when pedaling - crank axle is moving sideways. How can I fix this?
The bike has individual cartridge bearings -- not at all standard for a "real" bike, and a bit unusual for even an exercise bike.  (In fact, though I've seen a half-dozen different types of exercise bikes taken apart I've never seen anything like this.)

But it's not a terribly complicated setup.  The C-clips hold the axle in place.  The ring against which the C-clips ride is the inner race of the bearing and rotates with the axle.  If you can find a bushing (washer) of a suitable diameter and thickness it can be inserted between the C-clip and the bearing -- fairly easily accomplished by someone with moderate mechanical abilities.  You should only need the bushing on one side.  The one thing to be wary of is to get the crank arm back on tight, as a loose crank arm quickly destroys the mating surfaces.

A well-equipped hardware store should have a selection of bushings (and some spare C-clips, should the one on there be damaged or go flying across the room).

(There is also an old mechanic's trick:  You could work some coarse string into the gap, twisting it around the axle several times.  It should stay in place fairly well, without anything to secure it, especially if you dab on a little grease or petrolatum.)