While you can host files in loads of places, our favorite at this time is Dropbox.com
You get 2 gigs of space, and the interface is simple and easy to use.
Visit the site, create a simple account, and you can upload files.
Be sure to place any files into the 'Public' folder to share them on this forum.
Once your file is uploaded, mouse over the name of the file. A small arrow will appear, which reveals a menu. Click on 'Copy Public Link.' Click the "Copy Link to Clipboard' button. Now, return to the forum, and click the icon to 'Insert Hyperlink.' Paste your link, and you're done!
Other good options include http://soundcloud.com/
(for mixes) and http://www.filedropper.com/
You can also attach mixes to your post, though there's a 10 meg limit, and the files will download to the user's computer, rather than play in the browser. Also, guests won't see your attached files at all!