Update! In modern browsers, the click event will be fired for a tap, so you don’t need to add extra touchstart or touchend events as click should suffice.
This previous answer worked for a time with browsers that thought a tap was special. It originally included a “touch” event that actually was never standardised.
Unless you have a problem with:
$(document).on('click', function () { ... });
There is no need to change anything!
Previous information, updated to remove touch…
To trigger the function with click or touch, you could change this:
$(document).click( function () {
To this:
$(document).on('click touchstart', function () {
The touchstart event fires as soon as an element is touched, so it may be more appropriate to use touchend depending on your circumstances.