Navigation in TrenchBroom is quite simple and straightforward. You will mostly use the mouse to move and pan the camera and to look around. There are also some keyboard shortcuts to help you position the camera with more precision. Just like in Quake, the camera cannot be rolled - in other words, up is always in the positive Z direction and down is always in the negative Z direction.
You can look around by holding the right mouse button and dragging the mouse around.
To move the camera foward and backward, spin the scroll wheel on your mouse in the direction you want to head towards. If you prefer to have the scroll wheel move the camera in the direction where the mouse cursor is pointing at, you can check the "Move camera towards cursor" option in the preferences. To move the camera sideways and up / down, hold the middle mouse button and drag the mouse in the any direction. For tablet users, there is an option in the preferences that will enable you to move the mouse horizontally by olding while holding the middle mouse button. Finally, you can also move the camera using the WASD keys.
The camera orbit mode allows you to rotate the camera about a selectable point. To get an idea as to what this means, imagine that you define a point in the map by clicking on a brush. The point where you clicked will be the center of your camera orbit. Now image a sphere whose center is the point where you just clicked and whose radius is the distance between the camera and the point. Orbiting will move the camera on the surface of that sphere while adjusting the camera's direction so that you keep looking at the same point. Visually, this is the same as rotating the entire map about the orbit center. Of course, you are not actually rotating anything - only the camera's position and direction are modified. Note that, since up and down are always fixed, you cannot cross the north and south poles of the orbit sphere.
Camera orbit mode is very useful if you are editing a brush because it allows you to view this brush from all sides quickly. Its best to try it and see for yourself how useful it is. To invoke the orbit mode, click and drag with the right mouse button while holding the key. The orbit center is the point in the map which you initially clicked. Dragging sideways will orbit the camera horizontally and dragging up and down will orbit the camera vertically.
To center the camera on the selection, choose from the menu. This will position the camera so that all selected objects become visible. The camera will not be rotated at all; only its position will be changed.