-See - to view with the eyes.  

Can you see the writing?- ¿Ves la letra? 

Did you see the film?- ¿Viste la película? (use watch in certain tenses-I like watching seeing films )

-Look at - turn one's eyes toward something.  

The girl is looking at the painting- La niña está mirando el cuadro

-Watch- observe with eyes, over time (something that is happening). 

The kid is watching TV- La niña está viendo la televisión

She is watching the bird- Está observando el pájaro

-Stare at- look at intently or fixedly, often with eyes wide open ( usually with surpirse, alarm).

The boy was staring at me- El niño me estaba mirando fijamente

-Gaze at- look at intenly (with curiosity or wonder).

She gazed up at the clouds- Miró hacia arriba contemplando las nubes

-Peer at- to look at searchingly or with difficulty.

They are peering through the window- Están mirando con dificultad por la ventana

-Peep at- to look at furtively (often through a hole or crack).

He peeped through the hole in the wall- Miró furtivamente por el agujero en la pared

- Peek (in/out)-  to look at quickly and curiously (often furtively) or to protrude slightly from

The rabbits peeked out from inside the box - Los conejos se asomaron por la caja