This tutorial can be executed with a few clicks, but since the bracketing technique is not widely used and is usually supported by complex pieces of software, I thought it was worth describing the process.
If you have a high-contrast scene, with dark and bright areas, a single shot with the default settings of your camera will not give a good result. Bracketing is the process of taking three photos; one using the camera’s recommended settings, one underexposed, and one overexposed (many cameras can automatically shoot a bracketed series of pictures: RTFM). It is better to use a tripod so that each image is perfectly aligned with the others. You should also set manually the white balance and ISO sensibility.
You can then combine the three shots to get a picture where all areas have correct exposure. How? With Photoshop or with the “exposure blend” plugin for Gimp. Or you can get a decent result with Paint.net and the “Alpha Mask Import” Plugin.
Open the underexposed and overexposed pictures (I will not use the third one, you can combine only two pictures with this technique).
Copy-Paste the darkest over the brightest into a new layer.
Step 2 if you did not use a tripod
Open the upper layer properties window and select the mode “Difference”
If there is an alignment problem, you will notice white lines along the edges.
Select all the upper layer, select “Move selected pixels” in the tool bar, and move carefully the upper layer, pixel by pixel, using the arrows of the keyboard until the picture is almost completely dark.
Unselect (press Esc) and set back the layer mode to Normal.
Select the picture in the upper layer and copy it (Ctrl A ; Ctrl C). Then unselect all (Esc).
Open Effects/Alpha Mask… and in the settings window select only “Paste from clipboard”.
Since the alpha mask is the picture itself (from the clipboard), the darkest parts of the upper layer will become transparent and the corresponding parts of the brightest layer will appear.
Click Ok. You are done. The final picture is in the middle and is a mix of the two others (the wall on the right is rather bright but the sky is colorfull).
Note: For step 3, you can also use the Alpha Mask plugin from the Illnab1024's Plugins.
Bonus: What if you did not take a set of bracketed pictures? Open your only picture, adapt Brightness/Contrast to generate one overexposed and one underexposed and go to step 1.