In order to explain the grammar <동작돌사> + 게 되다 in class today, our teacher related her embarrassing experience in China. She was asking a native for direction and the reply she got was "我不清楚" (I'm not clear). It may seem rather simple for us, whom understand Mandarin, but not to our Korean teacher. She didn't know what "我不清楚" means and as she didn't seem to be getting any direction from the person, she went on to ask a second native. The second person replied, "我不太清楚" (I'm not too clear) and that totally confused her. As to what happened to her after that, she didn't tell us.
Our teacher didn't realise that both "我不清楚" or "我不太清楚" also mean "I don't know". This is because all she had learnt about saying "I don't know" in Mandarin was "我不知道" or "我不认识". "我不清楚" was out of her vocabulary range. Subsequently, as she heard more and more people saying "我不清楚", she started to guess that it should mean "I don't know" and finally, one fine day, she confirmed her guess. Using this story, our teacher started to explain the grammar. She didn't go out intentionally to search for the meaning of "我不清楚" but because she kept hearing people saying "我不清楚", she naturally came to know what "我不清楚" means. To summarise it, 그 말을 자주 들어서 알게 됐어요. (Because I hear those words frequently, I came to know its meaning.)
Now, back to the textbook explanation of the grammar <동작돌사> + 게 되다. This grammar is used when you want to say about the change that happens naturally as a result of certain situation or condition. The most important thing to note is that the change must happen naturally and not intentionally. Let's say you study hard with an intention to do well in the exam, this sentence 열심히 공부해서 시험에 잘 보게 됐어요 is a wrong expression. Instead, you should write, 열심히 공부해서 시험에 잘 봤어요 (Because I studied hard, I did well in the exam).
In life, many changes just happen naturally without any intervention. Despite that, for a change to happen naturally, there is still a need for an "initiator" or a spark. Frankly, I didn't quite understand this grammar until today. The "spark" that leads me to this understanding is my decision to repeat Intermediate-level Korean. 중급 한국어 수업을 다시 한 번 공부해서 이 문법을 알게 됐어요 (Because I study intermediate Korean again, I came to understand this grammar). To this point, it may seem that the grammar has been fully explained though not quite yet.
There is just one more thing to say, which is when to use 돼요 and 됐어요. I have been using 됐어요 in all my examples above because I am referring to a specific situation for each example. If I am referring to a general situation, the sentence shall end in 돼요. For a specific situation, change must have already happened before I can talked about it and hence the past-tense form "됐어요" is more appropriate. In a general situation, the change can happen anytime, be it in the past or the future, so the present-tense form "돼요" is preferred. For example, 날씨가 더우면 에이컨을 켜게 돼요 (If the weather is hot, the air-con came to be switched on). "날씨가 더우면" is a general situation which is being referred to and so 돼요 is used.
마지막으로 난 심심해서 이 글을 쓰게 됐어요. 혹시 너는 이 글을 읽어서 문법을 알게 되면 좋겠어요. 그럼 오늘 이만 쓸게요.