to watch / to make sure
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to watch
To follow or observe with your eyes what is happening, often without intervening yourself.
Wir sahen vom Fenster aus zu, wie die Kinder im Schnee spielten.
We watched from the window as the children played in the snow.
'Zusehen' (to watch/to make sure) is a separable verb. In a main clause, the prefix 'zu' comes at the end. In the infinitive with 'zu', 'zuzusehen' is written as one word.
Ich sehe dir gerne beim Kochen zu.
I like watching you cook.
When you watch a person doing something, that person is in the dative. You say 'Ich sehe dir zu' (I am watching you), not 'Ich sehe dich zu'.
Kann ich Ihnen bei der Arbeit zusehen?
Can I watch you work?
In the meaning 'dafür sorgen' (to make sure), 'zusehen' is almost always used with a subordinate clause that begins with 'dass' (that). The verb 'zusehen' comes directly before the comma.
Ich sehe zu, dass ich morgen alle E-Mails beantworte.
I will make sure that I answer all emails tomorrow.
In the imperative, 'Sieh zu, dass...' is often used as a colloquial, slightly urgent instruction to make sure that something gets done.
Sieh zu, dass du den Zug nicht verpasst!
Make sure you don't miss the train!
to see
'sehen' and 'zusehen' both have to do with the eyes. 'sehen' is the general word: you perceive something or watch something, for example a film. 'zusehen' is used when you observe what is happening, often during an action or event. Usually, you are not taking part yourself. The words can be confused because, for example, you can 'ein Spiel sehen' (watch a game) or 'bei einem Spiel zusehen' (watch a game as an observer). 'sehen' is more general, while 'zusehen' emphasizes watching from the outside.
Am Morgen sieht Tom seinen Freunden beim Training zu.
In the morning, Tom watches his friends during training.
Vom Fenster aus sehe ich den Bus an der Haltestelle.
From the window, I can see the bus at the stop.