I have just recently gone through this process so well basically this is what you need;
1 - Depending on where you live you have to go your respective area municipality - go to Baladiya website to find out this.. Mine was Al-Ryan as I live in Abu Hamour
2 - Original Contract 3 copies signed by both parties
3 - A Copy of owner ID card
4 - Copy of Tenant ID Card
5 - A Copy of Agency Or a Written NOC letter from the owner
6 - A Copy of title land and Map
If the owner of the property is company then you need this additional stuff:
7 - A Photocopy of Authorized Signatory Card
8 - A photocopy of Commercial record
9 - A Photocopy of Commercial permit
10 - Water and Electricity consumption bill
Also Note: Attestation of Partition is not allowed which means you need to be living in a Standalone apartment or Villa and the contract should be on your name.
I am writing is directly from the requirements paper I got from the Municipality Office.

Hope that helps and good luck.. I would suggest do it sooner rather then later because i was late by 3 months and have to pay penalty around 600QAR on top of the registration fee of the contract which is Annual Rent x 1%