Argue. If your partner says “this means X”, and you either don’t understand why or you have another opinion, demand an explanation.
Read to understand. Sometimes, when dealing with a chunk of text, it’s easier to figure out the middle *after* you understand what’s on both ends. Therefore, if a fragment of text has you stumped, try skipping over it and seeing if you can come back to it later. (But you still have to come back to it eventually.)
Read the text both “inside” and “outside”. An inside reading translates the text into English (or whatever your native language is) phrase-by-phrase; an outside reading translates a larger chunk into an idiomatic paragraph. If you only read inside, you can miss the forest for the trees; if you only read outside, you can fool yourself by making broad guesses and not verifying them with details.