Well, I suggest taking a look at the following sites:
There are also several good books out there that will give you all sorts of different perspectives on what can be done with XML. If you are looking for a general understanding of XML, I suggest downloading the XML specification from the W3C (there is also a good book in the Goldfarb series called "The Annotated XML" which is an annotated version of the specification). Otherwise, there are several good books out there that will give you a broad understanding of several of the most popular uses of XML.
One thing to note, however, is that XML is not something you "run", exactly... XML is only a specification for marking up information. Some people use it to store data (XML database, object database, etc.). Others use it to send Remote Procedure Call messages over the network (XML-RPC, SOAP, etc.). Still others use it to augment the handling and modification of other XML documents (XML Namespaces, XSLT, XML Schema, RELAX, Schematron, XPath, etc.). Some use it to define standardized document structures that are industry-specific as well as generic (ebXML, SMBXML, etc.) And other use it in ways that are similar to its SGML roots (XHTML, etc.).
XML is used in all sorts of ways. Many, many more ways than I have mentioned here, in fact. The uses for XML are nearly limitless. You just need to figure out if you need it. If you do, then see if someone has already done some or all of the work for you (why reinvent the wheel?). If so, use it (if you can). If not, write your own specification.
In order to act upon an XML document, you will need to also look into an XML parser. There are several out now and each have their own strengths and weaknesses. You can work with a DOM parser that will take an XML document and parse it into the DOM (I believe Microsoft's MSXML is the most commonly used DOM parser). You can work with an event-driven parser such as SAX or expat, where you set event handlers for each type of event and process the XML document as it's being parsed. There are other parsers out there as well, some are generic in nature while others handle specific tasks (such as XSL tranformations). Some considerations in choosing a parser are things like what platform you are running on, what language you are using, how large or complex the documents you will be dealing with are, whether you want to use something that is open source or not, etc. In the end, you are sure to find at least one parser that will fit your needs (or most of them, anyhow).
p.s. I just noticed that w3schools isn't replying at the moment... don't know why...