She asked me to wake her up at 6.

Literal

She [topic-は] me [to-に], six o'clock [at-に] please-wake [quotative-と] said.

An embedded request addressed to the listener: 'wake me up at six.' The ~てください inside と言った is preserved as the original speaker's polite request. 起こす is the transitive 'to wake [someone] up' — paired with 起きる ('to wake up [oneself]') as a classic transitive/intransitive verb pair. Note that the time-point に here marks the clock time (六時に) — a fixed moment rather than a span.