It seems like it ought to be an easy thing to do, but I can't figure it out.

How do I take a particular animation for a unit and assign it to some other action that the unit normally doesn't do? For instance ... let's say I have a Great Worker, and in the xml I give him the ability to do a Great Work like the artist. This works fine, except he just stands there and there's no animation for a few seconds, and then he just disappears. What if I want him to use his Surrender animation when he executes the Great Work? How would I do that?

I'm not sure about the case you mention above specifically, but some informations about animation in general is contained within this tutorial: http://forums.civfanatics.com/showthread.php?p=7833240#post7833240

It specifically covers adding combat animations (and a weapon) to a worker.

Maybe using esemjay's KFM-konverter (http://forums.civfanatics.com/showthread.php?t=263215) is easier and faster for that.

Holy geez that thing is awesome.

This opens up so many possibilities ...

But before you begin modifiing: Check with NifScope, if the animations work for the unit.