To create a new time warp curve, select "Create a New Warp" from the drop down list. This will create a new time warp curve that you can modify to create the warp you want. When you first create the warp it won't be connected to anything, so to be useful, you should then select some objects that you want to warp time on, and use the "Apply Warp to Selection" button. You can use the "Remove Warp from Selection" button if you later want to remove the warp from an object in your scene.
As you change the current time in your scene, the window will show you the warped and unwarped time for the currently active time warp curve you are adjusting. You can use the "Enable This Warp" check box to temporarily disable the time warp (to see the animation in real time) without having to disconnect the warp from objects.
"Select This Warp" will select the time warp curve itself to make it easier to modify in the graph editor. "Select Applied" will select all objects that the active time warp is connected to currently.
Time Warper tries to be smart about applying the warp even to history and shape nodes under your selection. Since it is written in MEL it is not as fast as the global scene time warp to apply, but it still works reasonably fast, and you can interrupt a long operation if you need to.
Time Warper can also create an "anti-time warp" which is a time warp curve that negates the scene global time warp. This can be useful if you have a scene global time warp and just want one specific object to run at real time. From the drop down list select "Create Anti-Warp". The time warp curve generated will try to negate the scene global time warp. Once created, the anti-warp works just like any other Time Warper warp curve, and can be applied to specific objects as needed. Note that it is not possible to create an anit-time-warp for all possible global time warps; specifically, if your global time warp causes things to go backwards in time, it will be impossible to automatically generate a correct anti-warp.
"Delete This Warp" will delete the time warp curve and the supporting nodes generated for it.
Please let me know if you have any questions or run into any issues with this script. I hope it is as useful for you as it has been for us!
Note that the script has been tested on Maya 2011 and 2012, but should work on any version of Maya.