In order to browse for a file you will need the OI File Manager App, found in the Marketplace.
If you type a url (or copy/paste from the browser) into the 'File Name' text box and hit 'Load', it will download the file and start playing it.
If you point it at a file (or a URL) with HTML tags, it will strip them out as it reads. This will eventually be an option that can be turned off.
This is my first Android project, I'm still learning, and it's far from complete. I'm only one person, so I haven't been able to test on too many platforms. If you run into a problem on your phone or if you have any suggestions, let me know and I will try to check it out.