If you have been used to using different Apple IDs for different apps in iOS 6, you can still do that in iOS 7, but some of the details have changed.
One of the first complaints that came in was about Find My iPhone, with several people writing in worried that Apple had done away with the ability to use different Apple IDs with the app. But there is a 'Sign Out' button on the first screen. Simply tap that button, and you will be able to use a different Apple ID for Find My iPhone.
(Aside: you really should be using Find My iPhone, especially with the new improvements to it that came with iOS 7, which make it harder for anyo