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/
Excellent explanation. I knew this on one level (that they were different cases), but your examples really brought it home.
No. deine is a form of a possessive determiner, not a case form of the personal pronoun.
dein- can stand in any of the four cases depending on the case of the noun that it accompanies, e.g. dein Vater - deines Vaters - deinem Vater - deinen Vater.
du, dich, dir--du is the nominative dich is the accusative case, dir is the dative case. If you're a Mac user you might like the program German Grammar. It is easy to use and an excellent reference. I don't know if there is version for the PC world.
Regarding the cases, the information behind the following links may help you to understand them better: