하지만 seems to be used most often with the informal style and 그러나 is usually used with the formal style, 그렇지만 is used with both the informal and formal styles. 근데 is a short form of 그런데 instead. You should know that. 근데 is usually informal, but 그런데 is not necessarily informal, and is perfectly fine for formal speeches and writings. Another way to say 'but' is adding "지만" after a verb or a noun like this: -그 여자는 예쁘지만 못됐어 = She is pretty but mean.

You use 하지만. And you use it like this: you say one sentence, then you begin the second one with 하지만 and the rest is the same. 나는 노래를 사랑해요. 하지만 나는 노래를 할 수 없습니다. Hope this helps :)

Oh, yeah. And it means "I like the song, but I cannot sing". :) 하지만 means "however" or "but". And in Korean you use two sentences for "but" :) Sorry, I forgot to say this :)