Ontology, metaphysics. Sciences? Of what, exactly? The vocabulary of commitment is one I've always found useful in explaining ontology: i.e. ontology refers to the kinds of entities one is committed to being. Does one's ontology admit supernatural beings? Or, if one is an atomist, does one only commit to the existence of atoms while everything else is an epiphenomenon? So to have an ontology is to have ontological commitments to the kinds of things that have being (while, presumably, ruling others out).
Metaphysics I think is best thought of in terms of explicating the status of those commitments. So traditionally, metaphysics had to do with the study of necessary beings, aligned with the temporality of eternity. In which case you're dealing with questions of modality and temporality. A different metaphysics might yield a different conception of both, so that one relaxes the commitment to necessity and pays more attention to contingency and the so-called sublunary aspects of 'becoming' and so on. The temporal question also bears upon issues of principles/beginnings (arche) and ends (telos): are there purposes to things? If so, where do they come from, and where do they lead?
Condensed, one can say that if ontology deals with 'what', metaphysics deals with 'how'. There's all manner of room for variation and recombination here of course, but as introductory guiderails these will work pretty good.