Hezbollah's present involvement began when rebels started attacking the "Lebanese villages" in the region near Qusair. Here some links about that:
Hezbollah Defends Shiite Villages In Syria War
On the Frontline of the Battle for Syria’s Lebanese Villages
Having helped to conquer Qusair - and with that protecting the "Lebanese" villages - raises the question about what next. This article (For Hezbollah, What is Victory In Syria?) discusses that question. In one speech Nasrallah anounced as his goal to end rebel presence in three regions: the Damascus’ countryside, which is home to the Sayyida Zaynab shrine; the Homs’ countryside, which includes the city of Qusair and surrounding villages; and the Qalamoun area, which includes the Zabadani region from where Lebanese Shiite areas are now regularly shelled. That raises the question whether it will be easy to quit once Hezbollah has gotten involved.