I've animated the location of a text object, and now I want to use that same animation on many other text objects at arbitrary times. How can I do this?
When you keyframed the locations on an object, an action has already been created
Note that the keyframes have absolute coordinates, I you're looking for relative changes you would need to offset them in the NLA-Editor (or alternatively change the origin of the individual text objects).
When you want start animations at different time offsets you would need to place them as Action-Strips in the NLA-Editor there you can move the strips to the time offset they should start (and even scale the duration).