How to get rid of All dust/specs on sensor and lens?

I have a Nikon D200, and when I use high f-stops, like f/22 the dust and specs are more in focus, and more noticeable.

Here is a sample image of what I'm talking about:

I'm currently using a micro-fiber cloth to clean the lens (front and mount side), and cleaning carefully the mirror. Is there's better or more safe way to do this YOURSELF?

Added (1). Oh, and is this a result from the lens being dirty, or the sensor?

Added (2). Thanks, but I prefer to not think while shooting, "fix in photoshop". And it doesn't really make sense to shoot 200+ photos and have to manually "fix" every shot…

When you're shooting at that high of an f-stop, you're bound to have specs that are more noticeable.
These can easily be taken care with post processing.
At f/22, you're getting a deep DOF, which also leads to dust showing up.
Do you have a dust blower than you can use? That may help. But again, when I come across this problem, I just take care of it in Lightroom 3 with the spot healer.

My current DSLR vibrates the sensor every time it's powered up and shakes the dust loose. I blow air round it with a Rocket Blower. I do nothing else to this sensor. My old DSLR locked the mirror up to allow sensor cleaning and again I would use a Rocket Blower to blow the dust away. For all I know you have the hands and the touch of Shrek and I can't tell you what else I did but I have the hands of a sensitive artist and I would clean the sensor another way. Obviously if you damage or scratch the sensitive sensor you'll ruin your camera. But anyway, to me it looks like the dust is inside your lens. It's called dust ingress and apart from taking the lens apart you're stuffed. The lens will still be good for probably even f/16 even with dust ingress. Don't take the lens apart yourself but sell it on Ebay and then add some money to that income and replace the lens, for some reason a used kit lens will sell on Ebay for nearly the same as an unboxed new one (dealers take the kit lens out the boxes all the time to make up different kits for their customers).

This is all just dust and crud on the sensor. It is fairly easy to remove.

First, try using a bulb to blow the dust of the sensor.

If you still have dust, you can use a sensor brush.

Lastly, you can use a swab with a special cleaning fluid from a company called Visible Dust to remove anything still stuck to it.

Edit:
Do not worry about scratching your sensor. You sensor has a protective filter over it. In the unlikely event that you do scratch it, you can replace it for about $200, but that is the worst case scenario.

You should clean the mirror too, just so dust from the mirror doesn't end up on the sensor, mirror dust is not visible in the final image.

It's likely to be sensor dust.

To clean the sensor, lock the mirror up, remove lens & holding camera with lens opening facing down, blow gently using a Rocket Blower into the body. NEVER blow into the body with your breath! Holding it this way will let gravity do some of the work.

If you have oily spots on the sensor, then it may need a wet clean - the Visible Dust kit is good.

I wouldn't recommend touching the mirror - unlike bathroom mirrors, the silvering is on the front surface of the mirror and its is very easily damaged.

That sounds like a dirty sensor…

You can get rid of All dust specs in the sensor by having it cleaned by a camera store, but eventually it may creep back in.

I have a cleaning pack (contains cleaning fluid, pec pads, and pec pad holder and little rubber bands). Though not as good as a professional clean, it does the job (as I can't really afford to have my sensor cleaned every 2 weeks). Make sure you get the right size for your sensor (either cropped sensor or full frame sensor).

As far as dust on the lens, use a blower brush and/or lens tissue.

Although it may work if you are careful, I don't recommend sticking a microfiber cloth inside the camera to clean it. I prefer to use a blower brush instead.