A nation without an effective central government, torn by multiple factions of insurgents and terrorists. Sound familiar? So how did Syria clean up the mess that was Lebanon? Did they massacre whole populations, or was it less extreme than that?
My own opinion is that they backed certain factions, used overwhelming force against others, and employed a system that basically gave militias more or less exclusive control of sections of the country (kind of like setting up sub governments within a weak national government). This was combined with a dwindling of outside support (weapons and money) for various factions during the 90s, and pressure from various Middle Eastern nations on the factions to stop fighting. The wiki article has a good summary.
I don’t think they really cleaned up the mess either. I think they merely put a lid on the civil war, and that most of the root causes for the war haven’t been adressed yet.