だけど、[sentence] [noun] + だけど、[sentence] [na-adj] + だけど、[sentence] [verb (plain)] + んだけど [i-adj] + んだけど
だけど means "but". At the start of a sentence it pushes back on what was just said. Inside a sentence it is だ plus けど, after a noun or a な-adjective, and joins two halves that pull against each other. Both uses are casual.
Inside a sentence, the だ of だけど belongs only after a noun or a な-adjective. A verb or an い-adjective takes けど directly.
At the start of a sentence, でも means the same "but" and is the more common word; だけど is a little more casual. しかし belongs to writing and speeches. In polite conversation, use でも.
With the explanatory ん in front, any verb or adjective can take だけど. んだけど sets up a topic or a request, and the sentence often stops there, leaving the listener to respond.
だけれど and だけれども are longer forms of だけど and sound a little more formal, but they are still plain speech. The polite counterpart after a noun is ですけど, or ですが.