You may want to review regular GCDs first.
Sometimes the GCD will have more than one term. This is good news for you, because that means it will usually be pretty obvious. For example, suppose you're given −x(y − 1) − 3y(y − 1). Then it should be clear that both terms have the factor y − 1, so the whole thing factors as (−x − 3y)(y − 1).