Here's a brief outline of the steps involved:

The first step is to create a new playlist of un-purchased songs, export that playlist, and then save it as text. When you open it up, locate the URLs for the audio files you want as ringtones; using those Web addresses to download the 30-second snippets of the songs.

Once the audio samples are downloaded, rename the tracks—giving them a name (while keeping the .m4p file extensions) that's more meaningful to you than Apple's obscure file designations. That way the tracks will be more easily recognizable for the songs they represent when you go to use them as a ringtone.

You’ll be able to do that last bit after loading the files onto the iPhone. Once they’re on the device, you simply pick the file you want to use as a ringtone just like you would with the ringtones Apple pre-loaded. The 30-second song previews you just added are now listed in Settings --> Sound --> Ringtone along with these other tones.