I have lost hours trying to find mosquitoes in my bedroom. I won't go to sleep if I hear one. This has happened so many times that I was able to refine my technique.

If you can't find the mosquito, make sure that your door and window(s) are closed, turn the light off, go back to bed, cover your body so that the mosquito can't bite you without you hearing it approach, have a flyswatter handy, keep the light switch in one hand and don't move. If it hasn't had a chance to eat yet and you haven't moved for a while, the mosquito will most likely attack within minutes.

At this point, you have two options:

You can let it draw blood. This will give you an opportunity to kill it while it's sitting on your skin distracted and very vulnerable. If you don't want to kill it while it's on your skin, turn the light on and try to see where it flies. It's likely to fly to the nearest wall and sit there to digest. A mosquito that has consumed blood is easier to spot with its big abdomen and is easier to kill.

If you don't want to let it draw blood, turn the light on as soon as you hear it. It's fairly likely to land on a wall near you or on the ceiling. Using a flashlight will greatly help you in your search. The light from the flashlight lights the wall from various angles and can produce a shadow that will make the mosquito easier to spot. It also helps you focus on a smaller area, so that you can sweep the room more thoroughly and methodically.

If the mosquito isn't on a wall or on the ceiling, it's probably hiding in a spot that will make it very difficult to find. Your best bet is to go back to bed and start again from step one in order to prompt a new attack.