That airport shuttle is located at Ground Transportation. It's very easy to get to, located next to the Taxi queue. You just walk up to the kiosk/desk, tell them what hotel you want to go to, pay 9sgd and they'll give you a ticket and tell you where to sit and wait.

It runs 24 hours and I have never had more than 4 people on the bus with me. Wait time is usually 5-10 minutes.

Sorry, wish I knew how to put a picture on here because I took a picture and have a brochure, but there is no website listed. Here is what the brochure says: "Booking: self booking at Ground Transport Desk in Arrival Hall..."

Changi airport is very easy to maneuver. When you get to the Ground Transportation area, look around and very near the taxi queue will be this kiosk. Huge airport but very easy to find. "Airport Shuttle Service" or "Ground Transport Desk Shuttle Bus" should get you to the right spot.