Switching from the traditional layout of cellphone with keypads and a screen to a touchscreen Android phone indeed put me in quite a struggling transition. What used to be an easy step in changing an SMS notification tone became quite a challenge for me in Android. Anyway here is how I managed to do it.
1) Using your phone that's connected to Wi-Fi, download the ringtone of your choice. Usually I get my tones in http://www.zedge.net/ or I create my own customized tones using the Ringtone Maker app in Android.
2) In your phone, go to My files > download and then locate your downloaded tone.
3) Press and hold the filename of your tone until the pop-up menu appears.
4) Press Move.
5) Choose Sounds > Notifications.
6) Once inside the Notifications folder, press Move here.
To see if your new tone has been incorporated in the list of default tones:
1) Go to Settings > Sound > Notification ringtone.
Normally, you would find your new tone there.
To separate notification tones from SMS tones, I use the Go SMS Pro app in Android and I change my SMS notification tones there.
