eXist-db is a great tool for learning XQuery: exist-db.org.
I'd start by checking out the Basic XQuery Examples on the eXist-db.org website. This suite of interactive tutorials shows you example XQuery source code based on already-loaded XML files, such as Shakespeare plays, and lets you run each query in the tutorial. You can also edit the sample queries to see how your changes alter the results. Just click on the "Edit" button beneath each source code sample, and it'll take you to eXide, a web-based interactive query editor, to edit the queries and run them. (As Adam notes in the comment below, eXide is a great tool in its own right for learning XQuery.) While you can't upload your own XML to the copy of eXide that runs on eXist-db.org, you can browse the included files (click on Open and log in with username guest and password guest) and craft sample queries against the files.
If you want to run queries on your own files, just download and install the eXist from exist-db.org; then you'll have eXide and the ability to upload your own XML for querying, as well as all of eXist's built-in documentation.
Another great set of tutorials on XQuery 3.0 (and now 3.1) is the XQuery 3.0 (and 3.1) Features demo.
If you have questions about eXist, I'd recommend joining the exist-open mailing list.
