Selection & Editing Modes
There are 3 Editing Modes in DEdit:
You can change the modes by clicking the corresponding icons (icons 3,4,5 on the quickbar). I suggest learning the keyboard shortcuts for quick rotation between Editing Modes.

quickbar buttons
Selecting Brushes or Objects
If you want to deselect selected items, push the U-BUTTON on the keyboard. Learn to constantly deselecting selections by pressing U-BUTTON. That way you make sure you don’t accidentally edit a brush or object you did not want to.
When DEdit starts it will be in single selection mode. To select multiple brushes or objects switch to multi selection mode (icons 1 and 2 on the quickbar).
Brush Editing Mode
Allows you to select brushes in the world. You can then resize the brush on the grid by hitting the side pointers or move it around by holding down the left mouse button on the pointer in the middle. If you have multiple brushes selected they all will be put into a quarter that got its own pointers. You cannot resize a brush on its edges. Resizing multiple brushes might deform them not aligned to the grid.

a selected brush with resize pointers
Geometry Editing Mode
Allows you to select the different surfaces of a brush. It’s very useful to apply different textures to different sides of a brush or selecting a texture you want to use elsewhere.
Let’s say you want to give one side of a brush a different texture. Select the texture from the texture menu and switch to Geometry Editing Mode. Hover the mouse over the surface you want to change and push CTRL+T to apply the texture.
What if you want to create a new brush with an already used texture but you are too lazy to select the new texture from the texture menu? Switch into Geometry Editing Mode and hover with the mouse over an existing brushes surface that got the texture you want to use for the new brush. Right click to open the context menu and click on Select Texture. Now create the new brush. This will increases your efficiency by a lot.

selected surface of a brush with geometry mode
Object Editing Mode
Allows you to select objects that you have added to the world. Use it if you want to select multiple objects in the world. Selected objects can be moved around by drag and drop in the view modes while holding down the M-BUTTON.
What if you want to change the color or multiple lights you have inserted into your world? Be sure to be in multi selection mode. Switch to Object Editing Mode and select the lights by holding down the T-BUTTON and clicking on them one after another. Now change their color in the Properties menu.

selected objects in the 3D View