Create the path for the text to travel along.

See Create and modify text on a path.

Move the playhead to the frame where you want to begin the animation, then press A to enable keyframe recording.

In the Layout pane of the Text Inspector, adjust the Path Offset slider (or the adjacent value slider) to the amount you want to move the text on the path.

A keyframe is added to the Path Offset parameter.

A positive value moves the text toward the right, and a negative value moves the text toward the left. You can enter values greater than 100% or less than 0% in the value slider. A value greater than 100% moves the text completely off the path to the right; a value less than 0% moves the text off the path to the left. In the following image, the Path Offset is set to 105%, so the text is completely off the right end of the text path.

Go to the frame where you want to place the next keyframe.

Adjust the Path Offset slider or value slider to reposition the text on the path.

Play the project to see the text travel along the text path.

Press A again to disable keyframe recording.