| It is very easy to do but kinda hard to explain but I will try my best.
Standard cigarette lighters are a 2 piece design with 1 wire that goes to the back of the lighter. The inner casing is tube that fits inside the outer casing which is also a tube. The inner casing is the tube that contains the bezel that is visible through the dashboard. You would slide that through the hole on the dash and slide the outer casing over top of it. The outer casing (the part behind the dashboard) screws onto the inner casing. When you tighten the two together that affixes the unit to the dashboard. There is usually only 1 wire that bolts to the back of the unit.
The only difficult parts is getting your hand with the outer casing up behind the dashboard without having to disassemble half of the dash and holding the inner casing so that you can tighten the 2 together.
Are you sure it is not the lighter filament? Alot of older lighters do not work because the filament is bad (the curly bit in the end of the light handle). You can buy a replacement filament in most autoparts stores $1-$2. Unless of course you are using the lighter for some other purpose such as powering a GPS, etc., then of course you have already checked and the lighter unit itself is not working. | 
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