To look at something is to point your eyes at something.
She looked at me.
To look after something is to take care of it. To look after somebody is to take care of him or her.
Small children need someone to look after them.
To look for something is to try to find it.
I am looking for my keys.
Look in on
To look in on somebody is to visit while passing.
To look on is to be a mere spectator
I was hoping that he would come and help me, but he just looked on.
Look out for = be on one’s guard; watch for
Look out for drunk drivers.
Look out for careless spelling mistakes.
Look up = improve
His condition has looked up.
Look something up
To look up a word is to try to find it in a dictionary.
One way of improving your vocabulary is to look up words whose meanings you don’t know.
Look up to = respect
We all look up to him. (= We all respect him.)