Shooting dark and bright areas together

There are two ways that are generally employed. The first is to use a Graduated Neutral Density Filter to reduce the amount of light entering the lens from the upper half of the frame but not the lower half. The reducing film on the filter is graduated from full strength on the top to no filter on the bottom so the effect is gradual not abrupt.

The second way is to take two images and blend them after the fact in the computer using Photoshop or one of many other tools available for this. It is called HRD or High Dynamic Range photography.

Hello:

Bracket the exposure.

In other words, Try 3 different F-Stops.

If your familiar With masks, You can use the Curtis Combo system.

It mounts on the lens barrel. 1 part of the mask put into a slot reduces half the exposure of part of the frame.

I don't know if Jack Curtis is still in business but here's his old address:

Jack Curtis 2231 Virginia Ave

Santa Monica, California 90404

You can also use a search engine. Search for the Jack Curtis Combo and advanced mask system

Hello:

Bracket the exposure.

In other words, Try 3 different F-Stops.

If your familiar With masks, You can use the Curtis Combo system.

It mounts on the lens barrel. 1 part of the mask put into a slot reduces half the exposure of part of the frame.

I don't know if Jack Curtis is still in business but here's his old address:

Jack Curtis 2231 Virginia Ave

Santa Monica, California 90404

You can also use a search engine. Search for the Jack Curtis Combo and advanced mask system

I agree with kenteroo.

There is also another way, but it is based solely on your camera. 

It's called SuperCCD. I bought a Fujifilm s5600 with this sensor. I's not perfect, but you can really feel the difference in comparison to other cameras, especially if you use additional software like LightMachine to extend your dynamic range.

Whenever you have an image with high contrast of light, the problem is to capture the full details of the well lit areas as well as the badly lit areas. The solution I know, is to create HDR photos using Photoshop or  other software.

 These photos (High Dynamic Range) are created using a few photos (over exposed to under exposed) together in order to create one photo where the photo has details in all areas of the image.

 see: Definition in Wikipedia, also HDR examples in Flickr.com

hope this helps.

Shoot it in the manual mode.

The first answer (by kenteroo) is excellent. I'd like to elaborate a little, though:

1. The first method described (using a neutral density filter) is applicable only if there is a clear straight line dividing the upper and lower parts of the scene. If the crag, for example, extends into the sky, then the filter would make the crag even darker than it already is.
    
2. HDR is a great technique (see example here). It requires that you take several consecutive shots (e.g. 3), each with a different exposure level (i.e. one normally exposed, one underexposed and one overexposed). You then use a special software such as Photomatix to combine the three shots. The best way to do this is by putting the camera on a tripod and setting the camera to "autobracketing mode", in which it takes three consecutive shots automatically with varying exposure levels. The problem is that very simple cameras may not have this autobracketing feature or even the option of manually adjusting the exposure.
    
3. HDR from a single shot (instead of from several combined shots) - this can be done if your camera can shoot in RAW mode. Again, this is something that many simple cameras cannot do.
    
4. Fill flash - adjust the exposure to the brightest part of the image, and use flash to illuminate the darker part. For example, suppose you want to shoot a person who is standing in front of a setting sun. Aim the camera to the bright horizon and lock the exposure (usually by half-pressing the shutter release button), then shoot with flash on. This will make sure the setting sun will come out nicely exposed (and not overexposed), while the flash lights up the person in the foreground. Of course, for this to work your subject has to be within the range of your flash (usually a few feet away).

I hope this helps. If you need any clarifications just let me know.