Look after
1) I am looking after my cat. It's ill now.
2) I can look after your house, when you're away.
Look for
1) I am looking for my cat. It has hidden somewhere and I can't find it.
2) I've lost my telephone and now I have to look for it.
Look out
1) I looked out of my window and saw snow.
2) Look out when you're on the road.