Tomorrow's my birthday — I'm turning 17.

Literal

Tomorrow [topic-は] my birthday [and-で], 17-years-old become [explanatory-んだ].

で here functions as a conjunctive — 'it's my birthday, and...' rather than instrumental or locative. 17歳になるんだ uses なる (become) + the explanatory んだ, giving the announcement an excited, sharing tone. 僕 is a casual first-person pronoun used mostly by males.