1. put aside / by = save money for future use
(aside often implies that the money is being saved for a certain purpose)
He puts aside £30 a month to pay for his summer holidays.
Don't spend all your salary. Try to put something by each month.
2. put away = put something tidily out of sight (usually in drawers or cupboards)
Put your toys away, children! It's bedtime!
3. put something back = replace it where you found it
When you finish the book, put it back on the shelf.
4. put back a clock / watch = go back 1 hour
On October 30, we had to put our clocks back.
Sometimes, this is used figuratively (as a metaphor) to mean "return to the customs of the past"
MOTHER: Your father and I will arrange a marriage when the time comes.
DAUGHTER: You are trying to put the clock back! Parents don't arrange marriages these days!
5. put down =
(a) stop holding something
He picked up the saucepan and put it down at once because the handle was almost red-hot.
(b) crush rebellions / movements
Troops were used to put down the rebellion.
( c ) write
Put down his phone number before you forget it.