In XCode I can specify Base SDK. I am wondering how does that work behind the scenes? If I am running an app, for example, on a device that has iOS 7 and my base SDK is iOS
Your project is built against the Current SDK. If you have an older Deployment Target, then your code base is compiled against that. So if you are building against 7.0, but have a 6.0 deployment target, iOS 7 specific deprecations will not be triggered. Everything will be compiled against the oldest specified deployment target.
This will however put the pressure on you as a developer to make sure you are not using iOS 7 specific code. The compiler will still assume you mean to allow newer users to run your application as well and that all the newest methods are available to you and your latest version users. You can either test your code base against the older SDK with older devices or Simulators to make sure it runs well, or use an application like Deploymate that will test for methods you are using that could potentially cause problems.
If you plan to use any of the latest methods, you will need to wrap them up in the compiler if statement (like Peter Fidemraizer answered) or in normal if statements checking the version in the Foundation framework.
if (floor(NSFoundationVersionNumber) <= NSFoundationVersionNumber_iOS_6_1) {
// Load resources for iOS 6.1 or earlier
} else {
// Load resources for iOS 7 or later
}