To see somebody do and see somebody doing

 

Olivier got into his car and drove away. You saw this. You can say:

- I saw Olivier get into his car and drive away.

So, somebody did something and you saw this = I saw somebody do something

- He fell off the wall and I saw this = I saw (past simple) him fall (base form of the verb) of the wall.

 

Yesterday you saw Kyara. She was waiting for a bus. You can say:

- I saw Kyara waiting for a bus.

Here we use the -ing form for the action we see. This is because we see the person when they're in the middle of the action. We don't see the complete action from start to finish.

Another example

- He was walking along the street. I saw this when I drove past in my car = I saw him walking along the street.