You take a part of any track that you can identify, like the lead melody or vocals, put it in your daw and make your own song out of it. For proper remixing you should have a few of the original parts at your disposal, not necessarily recreate them by yourself.
And if you do try to recreate the melodies and chords yourself.. Well then you need to know, ask, guess or look it up online if somebody transcribed it already.
Either way you need permission to remix a track, so if you get permission to do so I'm sure you could get a remix pack including midi files and some samples from the artist in question.