I have an iPhone 4 and just updated the software to i OS 7. Before I updated the software I had been able to close my running apps to keep from running down the battery. I can't figure out now how to close them. Is there a way or do theft close themselves or what?
You can kill running applications by swiping them upwards after double tapping the Home button.
You can also disable background app refresh (a new iOS 7 feature) by disabling it under: Settings > General > Background App Refresh.
Applications typically stay running as long as the OS has enough resources for it, until reboot, or until you manually kill them. Some iOS applications can run in the background while actively using your phone's CPU (music players are a good example). iOS may kill background applications to give a foreground application more resources.
Same way as before. But iOS does a great job of managing running resources for you, so if you have a decrease of battery life, it could be that the OS is to much for your phone to handle, depending on which iPhone it is of course. "Multi-Tasking" in iOS is really just recently used applications (which is where you double click home and swipe up) and the background app refresh works pretty well.
Ultimately though, iPhones are meant to be self-sufficient, even in the matters of running processes. I understand you thinking that apps running in the background are the cause in the decrease of battery life, but maybe it could be iOS 7. After updating my 4S, My already-bad battery life decreased even more, no matter what I did. So I guess you either have to get a new phone or suffer, because the new design of iOS 7 is just to much for older phones.