How do I install the trainer skewer on my bicycle?

Push open the quick release lever. This will loosen the skewer. Locate the cap at the opposite end of the skewer, and unscrew. Continue unscrewing the cap until it is completely detached from the skewer threads.
Pull the skewer straight out by pulling on the quick release lever.
Insert the trainer skewer into the wheel with the quick release lever facing the left side of the bicycle. Put the spring on with the smaller end aiming toward the wheel. Gently compress the spring with the cap, and slowly turn the cap just enough to get it attached without falling off. Put the wheel into the dropouts, and finish tightening the cap.