It was my father who made me who I am today.

Literal

Father [subject-が] me [object-を] present's me [into-に] did-for-me [emphatic-のだ].

Without the explanatory のだ ending, this is a plain factual statement. Xを Yにしてくれた = 'made X into Y as a favor.' 現在の私 means 'the present me.'