What are the current budget options for getting from Chinatown to KLIA2: Terminal 2 of Kuala Lumpur International airport?

Public transport in Kuala Lumpur seems to be improving faster than ever.

Also, since my first visit only a few years ago, Air Asia has moved from the LCCT (Low-Cost Carrier Terminal), now closed, to the new KLIA2.

Information therefore seems a bit fuzzy when I search the net.

I have plenty of time until my flight tonight so I'm more interested in the cheaper ways to get to KLIA2 than the fastest ways.