You need some kind of application to invoke the transformation. In this application, extract the query parameters from the URL and pass them as stylesheet parameters (global <xsl:param> values) to the stylesheet. The API for doing this depends on the XSLT processor you are choosing to use: look for a method such as addParameter() or setParameter(). You may find a packaged application to do the job, for example Saxon supplies sample servlet code SaxonServlet.java which takes a URL with parameters in the form described.
Author, XSLT Programmer's Reference and XPath 2.0 Programmer's Reference