Using Secure Shell File Transfer, how do I see more than just the files under my home directory on the remote machine?

On your local machine (Windows), across the top of the Secure Shell File Transfer window, there is a row of menu items that says "File Edit View Operation".

Click the "View" item. This will cause a drop-down menu to appear.

In that menu, click the box to the left of "Show Root Directory" or "View Root Directory/Files".

This will cause the tree view of the remote file system (on the left side of the window) to change, giving you a view of all of the remote machine's files, starting with "/" (the root directory) at the top of the tree.

Now you can navigate to any readable directory on the remote machine.