I cannot figure out how to hide a nested composition/layer during the main composition. I want to hide it at the beginning, show it during part of the video, and then hide it for the rest of the time. How is this done? Is there a better way of doing this? I'm a rookie with After Effects, so please keep your explanations in detail. Thanks.
You can treat a nested composition or a precomp in the same way you treat any footage. You can split the layer (Ctrl/Cmnd + Shift + D), or simply duplicate the layer (Ctrl/Cmnd + D) and adjust the in our out points of the duplicate (Alt/Option + [ or ]), set keyframes for opacity (T). This is extremely basic stuff. Have you read Todd's Getting Started with After Effects?
If you just want to show or hide a layer and still keep it in the composition then you use the shy switch. The shy switch has nothing to do with layer visibility, it just makes it easier at times to navigate around the timeline.