There's no function to get the date and time in XSLT 1.0. The usual solution is to pass it to the stylesheet as a parameter. If that's not possible (e.g. in the browser) then you could get it from a RESTful web service using the document() function.
Michael Kay
http://www.saxonica.com/
Author, XSLT Programmer's Reference and XPath 2.0 Programmer's Reference