Let's make a new background wallpaper out of the loaded image. We only need the KDE logo (the gear-wheel on the right), not the whole picture, so select the logo by drawing a box around it. Press the left mouse button, hold it down and move the mouse. A dashed box appears, marking your selection. Repeat this until you are happy with your choice. Then go on and cut the selected region from the image by choosing Edit->Crop from the menu bar or it's equivalent shortcut, Ctrl+C. Your workspace should now look like this:
Reduced to the essentials
If you are not satisfied with the cutting you can always restore the image's original state with Edit->Reset, or the shortcut Ctrl+R.