Creating a custom weapon is easy enough. Adding a single enchantment to it is no problem, either. But what I can't figure out is how to give a custom weapon more than one enchantment. The "Enchanting" drop-down menu only offers the ability to add one... so, does anyone know how to add more than this? I'd like to have a weapon that is enchanted with fire damage and shock damage, but so far I've only been able to add one or the other, not both.

You don't add more than one enchantment to an item. You add more than one effect to an enchantment.

You'll need to create your own enchantment with the effects you want. It's really easy too.
Go to the Magic branch of object window and select enchantments, then right click "NEW" in the list of enchantments.
http://www.creationkit.com/Enchantment

Ahh, okay. That makes sense. Thank you!