"You and I" are used as the SUBJECT of a sentence. You can also think of it as "We". You and I should go to dinner now. (We should go to dinner now.) You and I went to the park yesterday. (We went to the park yesterday.) "You and me" are used as an OBJECT of a sentence, You can also think of it as "Us". They gave a present to you and me. (They gave a present to us.) They couldn't find you and me. (They couldn't find us.)