1) Settings -> Battery -> and look at what are allocated the biggest percentages. You can reply here with a screenshot if you like.
2) Best -> Do a full factory reset and it should be back as new from the shop. Have a look online, the procedure is very simple. Then you can reinstall the apps, music and photos you need. Try it with the basic apps for a day or two before reinstalling everything as it is probably a bad application causing the phone to stay awake and draining the battery.
Take BACKUPS first of all your music and photos! Your Gmail account should sync phone numbers, calendar, emails, etc. and pull them all back when you login in again on the wiped phone.