The difference between `wake up at 7′ and `wake up by 7′ ?

When you wake up `at’ seven, you get out of bed at exactly seven o’clock. Not before or after seven, but exactly at seven.

When you wake up `by’ seven o’clock, you get out of bed at seven or a few minutes before seven.

Examples:  I told my mother that I would be home by 6:00 o’clock.* *Ganesh said he’d be back home by 7: 00 o’clock. He returned at 10: 00 o’clock
Source:  ‘Know Your English’ Series – The Hindu Daily, October 17, 2005.