To remove an old cylinder when you do NOT have the key, either take it to a locksmith or do it yourself by drilling out the cylinder from the key slot side. Any good drill bit can do it:
a. Remove back plate from lock mechanism.
b. Drill out enough of the center of the cylinder to create a void close to release pin.
c. Drive the release pin into the void you've created. Do not drill through the little release pin hole because you risk damaging the chromed lock body. Push old cylinder out from behind the front plate.
d. To insert a new cylinder, put the key in the cylinder, turn 90 degrees and press down on the brass retaining pin.
e. Next insert the cylinder into the lock and turn the key clockwise until the brass retaining pin springs out and secures the cylinder in the lock. 
Note: Although the fit may be slightly looser than the original it will still be fully operational.
Completed installation.