You use 'mon,ma', when something belongs to you. Like,
"C'est ma soeur" (it's my sister)
"Mon pantalon est parti" (my pants are gone)
'Mon' is used when the object you are talking about is male. 'Ma' is used when the object that belongs to you is female. (LA table, LE pantalon)
'Moi' is 'I', or 'me', it depends of the context:
'Moi, je n'ai rien reçu' (I, I haven't received anything)
'Cette table appartient a moi' (That table belongs to me)