Before coming to Singapore I was reading only good things about the local health system. It was praised as being one of the best and most modern.
However, due to the lack of really bad injuries, I've never really had a reason to visit a real doctor or the hospital here during the last two years.
How it Works in a Nutshell
You choose the doctor of your favour, make an appointment or just hop by directly (which can result in enormous waiting times), you get diagnosted and then...you pay. If it was a simple coughing examination, maybe 30 SD, if you got a complicated X-Ray maybe 400 SD. Be prepaired and bring money or credit cards. Later you will send the receipt/form you got from your doctor to your health insurance company and they will reimburance you. Its very important that you most probably only get your money back for "real" doctor examinations.
I once visited a local ancient chinese medicine practising doctor, getting my knee accupunctured, and some weird looking pills as subscription, but ran against closed doors when i was trying to file this in for reimburasment. (Read: Being Sick In Singapore)
Dont Go Alone
If your health problem is one that cant easily be described with hand and foot gestueres, then bring someone who speaks mandarin or cantonese. Although you might expect it, there a are a lot of doctors (yes, in the hospitals as well) that dont speak english and will amputate your arm when you need a xray of your foot. Not joking, a french colleague of mine had a bad bycycle accident and the local doctor told him to stay in bed until he feels better, when he went for holiday in french and saw a doctor over there he was on the OP table quicker then he could think of, his injury was a searious one and needed complicated operations instead of rest in the bed.
Following you can find details on Hospitals and Doctors situated in the city center / close CBD
This is the most frequented hospital in Singapore at a very central location. The webpage offers online booking of appointments, details about rates, doctors etc.
Raffles Hospital also offers several "outlets" that are located over Singapore, there you will find all the service and equipment as well and in case you just have a "normal" issue, it might be wise to go there instead of the (often very crowded) hospital itself.