What is the difference between dir and dich?
Du bist hier. - You are here. (nominative case, YOU/DU is the subject)
Ich liebe dich. - I love you. (accusative case, YOU/DICH is the direct object)
Ich wünsche dir viel Glück. - I wish you good luck. (dative case, YOU/DIR is the indirect object)
So DU - DICH - DIR, would go the same for ICH, MICH, MIR and ER, IHN, IHM, and so on.
There is also Genitive case but I would leave that for later :-)
Refer to this for more information on cases: http://germanforenglishspeakers.com/nouns/case/ and on pronouns: http://germanforenglishspeakers.com/pronouns/personal-possessive-pronouns/
Regarding the cases, the information behind the following links may help you to understand them better: