Welcome to Android Central! Where is the downloaded mp3 or wav file that you'd like to turn into a ringtone or notification? If you downloaded it directly to your phone, use a file manager app (like ES File Explorer) and copy or move the file to either the Ringtones folder or the Notifications folder. Then go to Settings>Sound, select Ringtone or Notification, and the new tone should be there. If it isn't, try rebooting.
If the file is downloaded to your computer the, you could either connect the phone to your computer via USB and use the computer's file explorer to transfer to the file to the correct folder, or upload the file to Google Drive from the computer, then download it from your Drive app to your phone. Then move the file to the proper folder using the steps above.