The following guide is based on my experience in Augutst and September 2017.
1. I went to Hamad hospoital in the morning but was told they would only do it from 16:00~21:00. On their website, they claimed they only do it in morning.
2. I went again in the evening. The lady asked where I live and then told me I had to go to Al Daayen Health Center (in Zone 74 near Al Khor) first to register. I live in Zone 65 in Dafna, near West Bay. It seems people living in a certain zone need to go to some particular health center first, but you wouldn't know which one to go. It is not necessarily the one closest to where you live. I am afraid the only way to find out is to go to Hamad Hospital in person with your address and ask them. In my case, Al Daayen Health Center is 30 minutes drive away, and it's very close to Al Khor.
3. I went to Al Daayen Health Center in the morning of the first working day after the Eid Holiday, and the guard told me the staff of card registration won't start working until the next Sunday and they only do it in the morning starting from 07:00.
4. I went back to Al Daayen the next Sunday morning, and was told by the card registration lady that they only did it in the afternoon starting from 12:00. Maybe because I was 9 monthes pregnant, they registered for me right away.
All I needed to show her was my QID, and I needed to tell her where I live (I have my address on the address proof by my property management agency).
She then gave me a form of health card application with a sticker on it. My personal info was on the sticker and I did not need to fill up the form even though it was full of blanks.
I was told to bring this application form together with the QID, a copy of the QID, a photo, 100 Riyal in cash to Hamad Hospital or West Bay Health Center(15 minutes walk from where I live) in morning from 07:00 to 12:00. To be honest, I was not sure if Hamad Hospital office would open in the morning based on my previous experience.
5. I went to West Bay Health Center the same morning, presenting all paperwork and cash, and they printed me the card straight away.

P.S.
* I applied the card for my husband at the same time, just needed his QID, a photocopy of his QID, his photo, and another 100 Riyal. No marriage proof was needed.
* No one ever asked for electricity or water bill to prove the address. But I had the property agency's statement just in case.
* It seems what they say on the Hamad Hospital website about applying the card is not the same as what I have experienced, expecially in the respect of where to go and when the office will be open. Even staff in different places are not 100% correct about thei working hour.
* It's hard to access any service call number to make enquiry; it is time consuming and frustrating to have to go to every office in person.