For example, in javascript
I can say
var x = 5;
Later I can do
x = \'a\';
and then
Python uses a technique called reference counting, which basically puts a counter in the value. Each time a reference to a value is created, the counter is incremented. When a reference to the value is lost (for instance when you assign a new value to 'x'), the value is decremented. When the counter reaches zero, that means that no reference to the value exists, and it can be deallocated. This is a simplified explanation, but that's at least the basics.
Well, those variables are references to immutable strings which are allocated at compile time.
Of course it depends on the VM, but in general, I think, most C-based scripting languages allocate a large block of memory, expanding it as necessary and do their own allocation within that, rarely if ever giving anything back to the O/S. Especially in a lexically scoped language, which almost all of them are, variables are all allocated dynamically within this block, not on anything analogous to a C stack, and they are freed with either reference counting or with a garbage collector.
If your scripting language is running on the JVM, or .NET, or something like it (Parrot?), creating a variable is merely the creation of something like a Java object. Some time after there are no more references to the object, the garbage collector will reclaim the memory.