Remove the chain cover from the pedal drive assembly. The exact mechanism differs from model to model, but on most Airdynes, the chain cover is held on by a series of Phillips head screws.
Locate the pedal drive assembly, where the pedals meet the drive train. You might wish to remove the pedals from the connecting arms to make access to the drive assembly easier.
Locate the chain tensioner, which runs perpendicular to the drive assembly. Look for two long pins which run through U-shaped brackets attached to the drive chain.
Twist the pins counterclockwise. You may need to hold the backing nuts in place to keep the mechanism from shifting.
Gently push the U-shaped brackets connected to the drive chain backward toward the rear of the bike until the chain feels tight.
Re-tighten the pins, and replace the chain cover and the pedals