Three forms:
けどcasual context.
か to make it moreformal
けれど is alsoformal.
Just like 「から」 and 「ので」, it is part of the first sub-sentence. This is unlike english!
but
indicates a contradiction; 'but'.
友達に聞いてけど、知らなかった I asked a friend, but they didn't know
今日は暇だけど、明日は忙しい。 Today is free, but tomorrow is busy.
だけど、彼がまだ好きなの。 (That may be so,) but I still like him
Introductory remark
When you want to say something, but you wish to clarify a topic (or give more information), you can introduce this with けど.
今日の夕飯だけど、お好み焼きはどう？ About today's dinner, how about okonomiyaki?
Matrixを見たけど、面白かった。 I watched the matrix, it was interesting.
Very often in combination with the explanatory の・んだ.
明日田中さんの誕生日会があるんですけど、行きますか？ Tomorrow is to Tanaka's birthday party, do you wanna go?
さっきメロンもらったんだけど、食べる？ I just received a melon, do you wanna eat some?
皆さん、今回の動画のテーマなんですけど、今回の動画は「けど」について話します。 Everyone, about the theme of today's video, I will talk about 'けど' in this video.
Also goes with が. It's considered good form to clarify your situation using the explanatory の before asking a question (or a favour).
ラーメンを食べたかったんですが, どこにいい店を教えてもらえませんか？ I want to eat ramen, could you tell me a good place?
午後銀行へ行きたいんですが、かまいませんか。 I wanted to go to the bank in the afternoon, is that a problem?
テレビの音が大きいのですが、音を小さくしていただけませんか。 The television's sound is loud/big, could you lower the volume?
けれど（も）
literally just a moreformal variant, which can be used for all other uses.
外は暑いけれど、家の中は涼しい the outside is hot, (but) inside it is cool. (very formal)
彼は若いけれども経験がある he is young, (but) he has experience. (very formal)