Stromboli is one of the most interesting volcanoes on Earth, having had an almost constant activity for centuries and centuries. In fact it used to be called the "lighthouse" of the Mediterranean...
When you arrive in Stromboli, there are various organizations providing guides who will lead you to the top of the volcano. My suggestion is to go with one of them, for Stromboli is known for its volcanic bombs too - some of which have killed toursist in past... Not that one should panic, but going with someone who does know the area makes the difference.
Among the various organisations on the island, there is one which has an excellent website, namely Magmatrek. Here you can find info on the volcano, a route map, plus insights on the flora and fauna on Stromboli, as well as a detailed chart illustrating what you might expect, weatherwise.
There are beautiful photogalleries here and here.