You posted under the ST01C timer.
ST01C has black, red and blue wires, and has a battery to run the clock.
You have black, white, red and green.
So your timer has an electronic clock and no battery.
Let's go through the wires one at a time.
You can add a comment and I will help further if needed.
Old switch has 2 black wires.
One of these wire is black-Hot
The other wire is black-to-Load (load is your light, fan, motor)
Black-Hot connects to timer-black wire
Black-to-Load connects to timer-red wire
NOW ... if these wires are reversed, the timer will not operate, so simply reverse the wires.
There are two wires to go:
Timer-green wire goes to bare copper wire.
Timer-white wire is the wire that runs the clock inside the timer. This is just like plugging in your alarm clock so the clock runs.
The timer-white wire connects to the other white wires located inside the box.
These white wires are usually twisted together and covered with a wire nut.
So untwist the wire nut and add the timer-white wire to these wires.
What if your box does not have these other white wires?
Then in that case, connect the timer-white wire to the bare copper and the clock will run.