Don't forget to wake me at 6 tomorrow morning.

Literal

Tomorrow [possessive-の] morning forget-not 6-o'clock [at-に] me [object-を] wake-up please.

Uses the 'don't X' form 忘れないで ('without forgetting') stacked in front of another ~てください request. The ~ないで form literally means 'without doing X' and works as both a manner adverbial and a negative request. Chaining it with the main verb 起こす creates 'wake me, (doing so) without forgetting' — more natural in English as 'don't forget to wake me.'