Using the eraser tool
The eraser tool allows you to remove pixels from a layer. Simply click and move your mouse around to erase things. By default, it removes only one pixel, but that can be changed its properties panel:

To change the size of the eraser tool:
Simply change the line thickness in the eraser tool's properties panel. The next time you erase, it will remove a square of that many pixels on each side.
See also
Changing tool properties
Setting a tool's pattern
Tools
Patterns