Who wrote the Indian Constitution? How were they selected to do the job?

India constitution was written by Drafting Committee of Indian Constitution. It was headed by Ambedkar but the persons were selected on their qualifications, experience etc like IAS officers, Advocates, Judges of those times, intellects, social workers etc I can name some persons from which you can ascertain the quality of people selected for this job.The committee members were:

Dr B. R. Ambedkar - Chairman

K M Munshi (Ex- Home Minister, Bombay)

Alladi Krishnaswamy Iyer (Ex- Advocate General, Madras State)

N Gopalaswami Ayengar (Ex-Prime Minister, J&K, member of Nehru Cabinet)

B L Mitter (Ex-Advocate General, India)

Md. Saadullah (Ex- Chief Minister of Assam, Muslim League member)

D P Khaitan (lawyer).

Sir Benegal Narsing Rau was appinted as the constitutional advisor.He later became First Indian Judge in International Court of Justice in 1950.

Other Committee members:

B L Mitter resigned from the committee. He was replaced by Madhav Rao (Legal Advisor of Maharaja of Vadodara).

D P Khaitan passed away and was replaced by T T Krishnamachar.

I just copied from Members of the Drafting Committee of the Constitution

upscguide.com

further reading Constituent Assembly of India