1. When you “too badly” want someone to do what you need and want when you are in a bad situation, or help is needed, you can use “제발.” ex)I would like you to correct my writing. Please. 내가 작문한 것 좀 고쳐주었으면 좋겠어. 제발.. ex)Will you do me a favor? Please. 제발 내 부탁 좀 들어줄래? ex)Please sit down. 제발 앉으세요. ex)Please don't leave me here alone 제발 날 여기 혼자 남겨 놓지 마. ex)]Please don't say any more about it. 그것에 대해서는 더 말하지 마시오 2.When what they are doing or saying makes you angry or upset and when you emphasize what you are saying, you can use “제발” as well. Please, come home. 제발 집에 돌아와.. Please, study English! 제발 좀 영어 공부해. Please, stop doing this! 제발 이것 좀 하지마. Please let us know if you are unable to attend. 제발 나올 수 없으면 알려 주세요 Please cool down 제발 흥분하지 마 3)when you hope that something that is going to happen never appear to happen, you can use “제발” as well. 안 일어나길 바랄 때.. ex)Please, stay with me. stay with me. 제발, 제발, 제발.. 눈 떠! ex)Please give me a break!! 제발 좀!! ex)Please don’t do this. “제발” 그러지마.

Um... I think no state for using 제발 in korean. But compare with 'please' 제발's meaning have some bad meaning. Some times it could be seing 'begging'. So if you use 제발 frequently. It not polite exression. You could be no confidence. any thing need help???

We don't say '제발' so often like in English. When you need to beg something and if it is desperate, you can use '제발'. 제발 좀 도와 주세요. Please, help me/ please I beg your help! 좀 도와 주세요 is enough for 'Please help me.' Jimmy's explanation is excellent, I just want to give you a bit more information.