How do I create a template to wrap an image around a cup?

Just for clarity, it sounds like you are not asking the usual - 'how do I warp my image around an image of a cup to simulate the image on a cup?' but rather 'how do I create a template that will be printed onto an actual cup by a printer?'

If the latter, then we need some further information.
Are the cup sides vertical or sloping? If vertical then you will need a document set up as a simple rectangle. If the slides slope then you will need the circumference at the bottom and top and the template will need some distortion. The hardest case, is a cup that does not taper smoothly but curves (like a typical teacup). That will need several careful measurements in order to make a template that will output your image in a distorted way but which will look correct on the cup.

Once you have a template (rectangular or distorted as required) then add a smart object for your image and warp the smart object into place, as described by Myra above.

You can save the document as a template (psdt file) and simply replace the image in the smart object when you want to change it.

Dave

You could make a Smart Object (Layer > Smart Objects > Convert to Smart Object or right-click on the layer and select Convert to Smart Object) to contain the artwork that could be swapped out and then apply Warp (Edit > Transform > Warp) to the Smart Object.

Whenever you want to swap the artwork, double-click on the Smart Object to open the PSB file that contains it, place (File > Place Embedded... or File > Place Linked...) your new artwork, either hide or delete the previous artwork, and save (File > Save...).