See, look, and watch

We use see when you notice an image without specially intending to. The image just enters your eye by chance.

I  saw a beautiful bird on the tree outside my house this morning

We use look when you deliberately move your eyes towards something (when you try to see something).

I looked out of the window this morning … (and saw a beautiful bird)

I looked at the tree …(and saw ….)

We use watch when we look at something for a period of time, or with concentration. We also use ‘watch’ when we look at something that is moving

I saw the bird, and watched it for several minutes

I watched the bird as it flew around the tree

I watched TV / a soccer game /

Could you watch over the baby while I cook the dinner, please?

So,

I looked out of the window this morning and saw a beautiful bird. I watched it for several minutes as it flew around the tree.

There’s a good explanation (with pictures) here in Japanese.