V + (으)세요 politely requests an action from someone:
지하철을 타세요. 더 빨라요.
Please take the subway. It's faster.
When used with 주다 (to give) it asks that someone act for you. Note that with verbs you use V + 아/어/해 주서요:
젓가락 주세요.
Please give me a spoon.
[좌회전 해 주세요.
Please turn left. (lit: please do a left for me)]
맛있게 드세요.
Please enjoy your meal. (polite form of eat)
비빔밥을 먹어 보세요.
Please try (eating) bibimbap.
다시 [한번 ] 말씀해 주세요.
Please say that again [once more ] for me.
Can you repeat that, please?
판 갈아 주세요.
At a restaurant: Please change the grill pan for me.
V + 지 마세요 is the negative form (지 being the particle of negation). It requests that you don't do something:
슬프지 마세요.
[Please don't be sad.]
잔디 위에서 걷지 마세요.
Please don't walk on the grass.
교과서 안에 쓰지 마세요.
Please don't write in the textbooks.