As far as I know the main difference between declarative and imperative programming is the fact that in declarative programming you rather specify what the problem is, while in imperative programming you state exactly how to solve a problem.
However it is not entirely clear for me when to use one over another. Imagine you are imposed to solve a certain problem, according to which properties you decide to tackle this down declaratively (i.e using prolog) or imperatively (i.e using Java)? For what kind of problems would you prefer to use one over the other?
Imperative programming is closer to what the actual machine performs. This is a quite low level form of programming, and the more complex your application grows, the harder it will be for you to grasp all details at such a low level. On the plus side, being close to the machine, you can write quite performant code if you are good at that.
Declarative programming is more abstract and higher level: With comparatively little code, you can express quite sophisticated relationships in a way that can be more easily seen to be correct.
To see an important difference, compare for example pure Prolog with Java: Suppose I take away one of the rules in a Prolog program. I know a priori that this can make the program at most more specific: Some things that held previously may now no longer hold.
On the other hand, suppose I take away a statement in a Java program: Nothing much can be said about the effect in general. The program may even no longer compile.
So, changes in an imperative program can have very unforeseen effects, and are extremely hard to reason about, because there are few guarantees and invariants, and many things are implicit in some global state of the program. This makes imperative programming very error-prone.