You should expect to see about a days worth of medium use out of a full charge on an S3. Maybe 8 ~ 10 hours if you stream a lot of media and have the screen on full brightness.
Some of the things that can drag a battery down are weak WiFi signals, widgets that poll a lot of data, automated task killers (don't use them!) and stuck services. The first thing you'll want to do is to charge your phone to full and then reboot it. Once it's fully booted, go to menu>settings>apps, click on the "running" tab and then toggle between "show cached" and "show running". If you have anything under running that you don't want, uninstall it.
If you continue to have poor battery life, you might have a bad battery.