Getting it onto the phone
The clip is the easy part; installing it is where phones differ. Android lets you copy an MP3 or M4A into the Ringtones folder and pick it in Settings. iPhone does not accept a ringtone file from a browser at all — it has to be installed through a desktop sync or a companion app, which no web page can do. If you are on iPhone, save the clip here and finish the job in that app.
Why a fade matters
A clip cut straight out of the middle of a song starts and ends on whatever the waveform happened to be doing, which is usually a click. A short fade at each end removes it. Fades here are 30 milliseconds unless you are cutting on silence, which is short enough that you will not hear it as a fade — only as the absence of the click.