I recently got my HMC, following is the process followed by me:
-- Went to Hamad Hospital to know how to make new card for me and my family, they redirected me to Mesaimeer health center ( I live in al sadd area).
-- Went to Mesaimeer HC, they asked me to go to Abu Nakhla. (AlSadd Zone falls in Abu Nakhla area).
-- Went to Abu Nakhla, and they registered my application, then asked me to go to AlRayyan Health Center to collect/print health cards from there.
-- I got the cards from ALRayyan HC.

As a first step, you can go to hamad hospital or Mesaimeer HC to know where you have to go for card registeration..

Regards..