How do I change the aperture when my camera is in manual mode

When you are in MANUAL mode you can change the APERTURE (F-stop) and SHUTTER SPEED (time) Yes you SHOULD be able to set the Aperture to F/22. You should be able to change the F-Stop too..

In aperture mode TA, you only can change the aperture manualy. The camera will try to set everything else, like shutter speed and ISO, according to what the camera thinks is the best. Will look at the scene and focal length. The amount of light should be enough according to you ISO setting.
In manual, M you have to do everything yourself. You can get under or over exposed pictures. When you choose "wrong" settings. But what is wrong? You decide what part of the photo has to be correct, even when the rest is to dark or to light. It could be you did setup the camera to warn you when over or under exposure occurs. I'm not that familiar with the canon DSLRs to be 100% sure, but I would look there.
again, aperture mode is not a manual mode and the camera needs enough light so it can manoeuvre in the settings you made.

Only in the Aperture mode and in Manual mode, you can choose the desired Aperture. It is all in the manual page 53, 54 and 55.
You can change Blurring / sharpening of the background (this most of the time will change the Aperture) you can change the brightness (will change the shutter speed) and you can add some image effects and choose for single shot, continues and self timer.
You can't directly choose for changing A, or S.

Do you mean set the aperture at f/11?

If you want the camera to set the shutter speed for proper exposure, turn the mode dial to the A position for Aperture Priority. Press the +/- button to display the shutter speed and aperture. Press cursor-up/down to change the aperture and the camera will change the shutter speed to give the proper exposure.

If you want to set the shutter speed and aperture yourself, turn the mode dial to M for Manual. Press the +/- button. Press cursor-up/down to set the shutter speed, cursor-left/right to set the aperture.

Full details are in the Shooting Mode section of the manual.

It depends on the lens.

If you're using a lens with an aperture ring, simply set the exposure mode to Manual or Aperture priority and change the aperture by turning the aperture ring on the lens. In Aperture priority the camera will set the shutter speed appropriately, in Manual you have to determine the appropriate shutter speed. If you want to use such a lens in Shutter priority or one of the Program modes, you must set the aperture to its smallest setting (largest f/number) and lock it.

If you're using a lens without an aperture ring then it's a bit harder. You can only use the camera in Shutter priority or one of the Program modes. You turn the command dial on the camera to change the exposure, and the aperture will change. If you want to use an exposure different than what the meter suggests, you can adjust it by using either exposure compensation or changing the ISO setting (or both).

If you need a manual, you can download one from
http://butkus.org/chinon/nikon/nikon_n6006af/nikon_n6006af.htm

You need to understand the relationship and teractivity of aperture, shutter speed and iso. In Av mod, you choose the aperture and the camera makes thw shutter speed agjustment, In Tv mode, you set the shutter speed and the camera makes the aperture adjustment, In manual, you have to set both shutter speed and aperture manually. If the ISO mode is set to AUTO, the camera chooses the sensors sensitivity to light automatically. Change to specific ISO
(200-400 for daylight and 799-1600 for night). Take a picture in AV mode and note what shutter speed the camera chose. Then switch to TC mode choose the same shutter speed and see if camera chose the same aperture(f-stop) you chose in first shot. Change to Manual and choose same f-stop and shutter speed the camera chose for you in the other modes. Compare all three photos. They should be almost if not exactly the same exposure wise.
In Tv mode choose a dlowers shutter speed, In Manual choose a combo of slower shuuter and wider f-stop(smaller number). Read your manual.

Turn the mode dial to "A". Turn the jog dial to change the aperture and the camera will change the shutter speed to match. You can also go to the manual mode, where you have to set both the aperture and shutter speed.
Full details are in the "How to use the APERTURE PRIORITY mode" section of the manual (page 22 in my copy). If you need a copy of the manual, you may download one here.

Not knowing your experience level, I want to make sure that you are (in the Manual mode) attempting to change the aperture by holding the aperture button with your thumb while rotating the main dial to increase or decrease the aperture value. If you are doing this, and the aperture value isn't changing, the camera needs service. You are probably still under warranty, so this should not cost you anything.

If you're in the USA, you can set up the repair service yourself at this link.

It depends on the exposure mode.

In Program mode (P), turn the command dial and the camera will shift the exposure by changing both the aperture and the shutter speed.

In Aperture-priority mode (A), turn the command dial and the camera will adjust the shutter speed to suit.

In Manual mode (M), hold the aperture button and turn the command dial.

If you're using a lens with an aperture ring, turn it to its smallest aperture (largest f/number) and lock it.