Ok. Load up Radiant and arrange the windows as in the screenshots below (you can drag the borders of the windows around to re-arrange them).
Next, use the left mouse button to draw a large square in the main plan window. You should see this appear in the 3D view as a flat slab. Press Escape to de-select the flat square bush you have just created. You can move around in the 3D window to get a better look if you like.
Now you need to stretch the brush into a cube. To do this hold down shift and click (left mouse) on the brush in the 3D view (This is the easiest way to select a specific brush in your map). The Brush should highlight again (in red). Now you can stretch the box upwards. To do this use the Z-Axis window (on the left), click just above the top edge of the box and drag upwards. If you click and drag within the box then the whole box will move rather than the edge, this is how you can reposition brushes and objects in the map
When the brush is shaped like a cube use the csg hollow tool 
to remove the core from the box and leave you with a boxy room (see below).
You can move the camera around in the 3D view to examine the room you have just made, but to spice things up we need to add some textures to the walls and floor. First we need to load a set of textures into Radiant. So go to the texture dropdown menu at the top of the screen and select the base_wall option. You should see the textures for this set appear in the texture window of Radiant.
Next, you need to select the walls of your room ready for texturing. However now the room is hollow its no longer a single brush, there is a new brush for each wall. Use Shift and the left Mouse button to select all 4 walls (You can do this in either the plan view or the 3D view but you may need to rotate the 3D view while doing this). Once all the walls are selected (highlighted in red) you can select a texture for them. Scroll through the texture window until you find bluemetal3b click this to apply it to the selected brushes.
Now we can repeat the same procedure for the floor (remember to press escape to deselect the walls). Try using metalfloor_wall_11. Now we need to do the ceiling, so select the roof brush and load in the skies set of textures from the dropdown menu. Pick pj_arena4_sky. Not only will this add a nice sky to our room but it will also create some basic lighting so we can see our map in Quake3 (without it the room would be pitch dark!).
Adding the player
Now we have created a room we need to pick a place for the player to start. Move the mouse to the centre of the room in the plan view and click the right button, a menu should appear. (make sure you have nothing selected before you do this by pressing escape). Select the option info from the list and then info_player_start. A red box will appear in the map where you were clicking, this represents the starting position for our player. You can move this object just like a brush, so make sure that it isn't stuck in a wall or a floor ( a few units away from walls and floors should be enough) and then hit escape to deselect it.
Our map is now ready to be compiled for quake. Make sure you save the map as "mymap1" using the file dropdown menu and then select the bsp_FullVis option from the bsp dropdown menu. A window will appear and Radiant will start compiling the map into a .bsp file that the main quake3 program can read. This process can take a while (especially for complex maps) and essentially is how quake compresses and maps and calculates lighting e.t.c.
When the process has finished we can test out the map. Launch quake3 (you can quit Radiant first if it is more convenient). When the program has loaded access the console by hitting ~ (tilde) and type the following./sv_pure 0 This allows you to test unofficial or unfinished maps. Then type /devmap mymap1 you should be thrown into your new map. If this doent happen make sure you have typed the commands correctly and named the map file correctly too.
Now we have created a basic room we can move on to examine more detailed aspects of lighting and introducing game objects.
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