Please wake me up at 6 tomorrow morning.

Literal

Tomorrow [possessive-の] morning 6-o'clock [at-に] wake-up please.

The pattern ~てください is the standard polite request. 起こす is transitive 'to wake (someone) up,' distinct from its intransitive partner 起きる ('to wake up [oneself]'). The object 私を is omitted — Japanese doesn't need to say 'wake me' when context makes it obvious.