You cannot download ringtones directly from the Internet to iPhone.

This is why to download a ringtone you need to do this from your computer or laptop.

1. Download a ringtone to your computer:

If you visited meloboom.com from your phone - log in and add ringtones you liked to the favorites
Visit meloboom.com from your computer, log in and visit the favorites.
Download the selected ringtones to your computer in M4R format (ringtone format for iPhone)

2. Transfer a ringtone to iPhone:

3. Select a new ringtone:

You can also set a ringtone for a particular contact: