Most phones allow you to assign specific ringtones to contacts. To do this, go to your contacts, select the contact you want to assign the ringtone to, then change the ringtone in the contact's settings.
Yes, some sites and apps, like Audiko, allow you to create custom ringtones using snippets of popular songs. This allows you to have a unique ringtone.
The steps to change your ringtone depend on your phone model. Usually, you can go to the ringtone settings in your phone settings and select the new ringtone you downloaded.