>From what I understand you can use XSL through an up-to-date web-browser to output data from an XML file to the browser.

IE5 and later will do client side translations of XML if you give it a path to an XSL stylesheet.

>Is this the best way?

No, not usually.

>If you had an ASP for example, can you include an XSL-Stylesheet and XML file directly into the ASP?

I think so, but it is more common, IMO, to apply the XSL to the XML on the server side and serve the results.