I've noticed that while sitting in traffic (when the car is not moving), the air conditioning start to get warmer (it's still cool but not as cold as a moment earlier). I figured it might be the cooling fan malfunctionaing and found out that only one is on (running) when I turn the AC on.
Oooo, not good. Both should run.
The fan on the left of the car operates, but the fan on the right does not turn on at all.
Left and right on any car are always determined from sitting in the drivers seat.
Do you want to change this line now?
I just wanted to know if BOTH fans are supposed to be running at the same time
With the AC on, yes.
Would this affect the cooling of the engine as well?
Hope I don't need a new fan...are they expensive?
Only if you are broke.
When a fan goes out, it usually blows its fuse. Check it. If it is blown, and there is no obvious wiring damage, you can probably assume it needs a fan motor.
Radiator fan: http://www.hondaautomotiveparts.com/...OR+%28DENSO%29
Condensor fan: http://www.hondaautomotiveparts.com/...DENSER+%281%29
You should look up your own car, I just guessed at one. There may be multiple choices.
The radiator fan is usually the one in front of the trans, condensor fan is usually in front of the engine. You may be able to count the blades on the fan and compare to the pics too.