It's not entirely clear whether you're asking about the philosophy of what's built into C++, or how to use it in a way that prevents memory leaks.
The primary way to prevent memory leaks (and other resource leaks) is known as either RAII (Resource Acquisition Is Initialization) or SBRM (Scope Bound Resource Management). Either way, the basic idea is pretty simple: since objects with auto storage duration are automatically destroyed on exit from their scope, you allocate memory in the ctor of such an object, and free the memory in its dtor.
As far as C++ itself goes, it doesn't really have a philosophy. It provides mechanisms, but leaves it up to the programmer to decide which mechanism is appropriate for the situation at hand. That's often RAII. Sometimes it might be a garbage collector. Still other times, other times it might be various sorts of custom memory managers. Of course, sometimes it's a combination of two or all three of those, or something else entirely.
Edit: As to why C++ does things this way, it's fairly simple: almost any other choice will render the language unsuited to at least some kinds of problems -- including a number for which C++ was quite clearly intended to be suitable. One of the most obvious of these was being able to run on a "bare" machine with a minimum of support structure (e.g., no OS)
