The Consumerist has the short and sweep scoop on the matter, which essentially involves trimming an MP3 to a small size and sending it to your phone by emailing it as an attachment to your phone at yourphonenumber @vzwpix.com.
When I tried this a while ago on my Motorola E815 (seen at right), I found issues with using Apple's Mail program (the phone didn't recognize the attachments correctly) but Google's GMail worked as expected. The instructions at The Consumerist say you have to change the file's suffix to .mid, but I found it worked fine with .mp3 as well. Your results may vary.
Now, if you'll excuse me, I've got to finish my collection of 80s TV theme songs ringtones with MacGyver and The A-Team .