There's also another article in the FAQ but I can't seem to locate it.
They used alarm clocks.
The typical image of an alarm clock with the two little bells on top is from the era of mechanical windup alarms. It required no electricity.
There were two springs to wind up. One was for the time keeping mechanism, and the other was to power to little hammer that wiggled back and forth between the bells when it was time to get up. The second spring stored enough energy to ring the bell for less than a minute, and you probably wanted the clock to keep ticking after the alarm went off.