Well, you cannot get all three out of ‘easy, cheap, quick’ so you’ll have to pick and choose. The Wikitravel entry on Kuala Lumpur has a comprehensive list of options available to get from the airport to the city (same article that you linked to, different section).
Kuala Lumpur has a vast urban train network but the confusing part is that they are all different ‘lines’, separate systems you need to buy separate tickets for. Most of them pass through one main station called KL Sentral, so if you can get there from the airport, you will be able to connect to any other place within the city. Essentially, you have three options:
Train / bus services start at 5am and go on till midnight, so plan accordingly. Unlike what it’s name implies, KL Sentral isn’t geographically central to KL city so if you’re staying in Bukit Bintang or Chinatown or the KLCC (city centre / ‘downtown’) area, you can get a train on of the other lines.
Credit:stackoverflow.com‘