[verb (plain)] + けれども [verb (polite)] + けれども [i-adj] + (です) + けれども [na-adj] + だ / です + けれども [noun] + だ / です + けれども けれども、[sentence]
けれども means "but". It goes at the end of the first half of a sentence, and the sentence carries on. A verb or an い-adjective takes it directly, in the plain or the polite form; a noun or a な-adjective needs だ or です in between.
All three mean the same. The longer the form, the more formal it sounds: けれども suits a speech, a business conversation or a letter, けれど is a step down, and けど is everyday conversation. In formal writing, が is the usual choice.
けれども does not always contrast. It also sets up what comes next: an apology or the topic first, then the request. The sentence can stop at けれども and leave the rest to the listener.
At the start of a sentence, けれども means "however", a more formal でも.