The simplest way of doing it is the proper LGB kit, part 68333 - it's listed here on Dragon's website:
http://www.dragon-gscale.co.uk/lgb-68333-interior-lighting-set-flat-connector-2008-p.asp
.... though they seem to be out of stock - a quick google search on the LGB part number should bring up some places who actually have them in.
One of these kits per coach will give you a single bulb in each coach, including all the cables to plug into the loco socket and then "daisy-chain" the coaches together.
The only downside of these kits (aside from having to buy them in the first place) is that they are 24v bulbs, and the lighting will be voltage-dependent - at low throttle settings you'll only get a dull glow, and the lights will only get bright when the train is running quite fast. To get round this you'd need to start fiddling around with voltage regulators and using 5v bulbs - lots of folks on here can tell you how if you wanted to go that route.
Be aware that there are many other ways of lighting coaches, including some very cheap ways of doing it with strips of stick-on LEDs (I've done ones with 3 LEDs, a switch and a 9v battery per coach for just a few quid each) - but as you're just starting out the proper kit may be the simplest way for you at the moment, as it's all built to fit properly and easily.
Jon.