The easiest way to caption photos is to log in, find the Photo Tools Menu underneath the main image on the page in SmugMug viewing style, and select Edit Captions/Keywords.
You'll see the following:

The original file names of the photos are displayed for convenience, and cannot be edited. They can, however, be displayed as captions in your galleries. See the Customize Gallery help section.
Your caption may be up to 65,000 characters long, so go ahead and tell the whole story. Want fancy captions?
Keywords? They're hot!