When do fish sleep?
They sleep at night time like us, which is why it's important to turn the lights off at night.
How can you know if they're sleeping or not?
It's harder to tell because they don't have eyelids like us, but they go in to a state where their brain activity shuts down 75%, the rest of the 25% used for staying afloat vertically on one spot and breathing. It's their state of inactivity and "sleep," the time when they re-energize their bodies, grow, and heal, just like us. If the lights are off, try prodding at the glass with your nail, just barely making a sound. If the fish is unresponsive, he / she is in sleep mode.
Once, when I came down in the middle of the night to get a glass of water, I accidently turned on the lights ( Oops! ). When I looked at the fish, they were swimming towards me like always, but they were extremely lazy, I could tell that I had just woke them up.
Do you know what a fake anemone is ? Some fish sleep in these. My goldfish did. One day I bought it and put it in the tank, next morning, there were 3 goldfish butts sticking out of it ! So I guess for some fish, it's like a bed. Try getting your fish one ( get the FAKE ones, not the real ones ).
Since they don't have eyelids, do they wake up easier than other animals?
Yes, they do wake up easier, as since their eyes are open, they are practically being forced to see things even if they don't want to. It's mostly light that wakes them up faster.