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:
- KLIA Ekspres: This is the fastest way and takes about 30 minutes to get to the KL Sentral. It is also the most 'expensive' option at MYR 35 (~$10) one-way. The express train goes non-stop from KLIA to KL Sentral. Also, certain airlines offer in-city check-ins for KLIA Ekspress ticket holders at Sentral, so this is an option you should check whether your airline offers in case you're running late.
- KLIA Transit: Costs the same as Ekspres if you're going KLIA-Sentral, goes along the same route, but it stops at a few more places in between so it takes slightly longer. One important stop is Bandar Tasik Selatan - the new inter-city bus transportation hub (it's almost as nice as any airport!) - so in case you want to catch a bus to another part of Malaysia, you get there directly from the airport.
- Bus: There are a couple of bus companies (SkyBus, AeroBus, etc) that offer MYR 10-15 tickets to the city (dropping off at KL Sentral mostly). This can be convenient if your flight lands at the low-cost terminal 'LCCT' (if you're flying in international with Air Asia, they operate a bus service of their own), as you don't have to transfer to the main terminal and can get a bus direct to the city. The drawback is that in peak traffic hours it can take up to two hours to get the city. The buses themselves are quite comfortable though.
- KTM Komuter: KTM Komuter is part of the city's train network too, and is the cheapest way to get to KLIA. Go from KL Sentral to Nilai, and then catch a bus from there - should cost you about MYR 8 all together. Yes, it's almost the same price as a bus ticket but depending on the time it will get you faster; early morning and late night are usually better times to take Komuter as it's not as crowded. Unlike local trains these aren't bad at all, they are all air-conditioned and have seating. This line also has more stops, so it might be closer to your destination. I usually go for this an option, but it isn't a good idea if you have heavy luggage with you.
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.