Blaming someone for a problem is finger-pointing. If none of your friends will take responsibility for breaking the neighbor's window with their baseball, there may be a lot of finger-pointing.
Finger-pointing can simply mean assigning blame to the guilty party, but it can also be a way of avoiding responsibility. If there's a large group of people at your house and someone accidentally lets the cat out, making your sister angry, there will very likely be some finger-pointing: "Tom kept leaving the door open!" You don't have to literally point at a person to be engaged in figurative finger-pointing, but it might be tempting when you say, "She did it!"