This chronology is an explanation of series of events, actions and decisions officially announced and undertaken by the Government, some highlighted milestones related to control of Covid-19 outbreak in India and the resulting outcomes.
Feel free to contribute the missed points or pointers, which got skipped in this timeline, you may comment on the article with reference source.

January 30^th 2020
First Covid-19 Positive Case was confirmed in District Trissur (Kerala), a student who had returned home for a vacation from Wuhan University in China.

February 02^nd 2020
Another Case (2nd) reported in Kerala’s Alappuzha District
February 03^rd 2020
3rd Corona Positive Case reported in Kerala’s Kasaragod District

March 02^nd 2020 / March 03^rd 2020
Union Health Ministry reported two covid-19 positive cases:
45-year-old man in Delhi who had travelled back from Italy
24-year-old engineer in Hyderabad who had a travel history with the United Arab Emirates
An Italian Citizen in Jaipur, who earlier tested negative, tested positive
Total Positive Covid-19 Case Count in India reached to 6 (Six)

March 03^rd 2020 / March 04^th 2020
Wife of the Italian tourist in Jaipur also tested positive
March 06^th 2020
International Passenger Screenings at Airports (GoM ordered all international passengers to be screened upon entry to the country)
Resident of West Delhi, who had travelled to Malaysia and Thailand, was diagnosed with the virus
March 11^th 2020
Suspended visas for travellers, including visa-free travel from 13 March until 15 April, except those on diplomatic, official, employment and project visas. Even travellers allowed to enter will be subject to quarantine orders.
March 12^th 2020
First confirmed Covid-19 Death in India
March 20^th 2020
Bollywood Singer, Kanika Kapoor who returned from London tested positive in Lucknow
Twelve more cases were reported in Kerala – Ernakulam (5), Kasaragod (6) and Palakkad (1)
In Bhilwara, Rajasthan, six people tested positive
A couple who returned from Spain, tested positive in Jaipur
18-year-old-girl in Telangana with a travel history to London tested positive.
Three more cases were reported in Maharashtra – Mumbai (1), Pune (1) and Pimpri-Chinchwad (1)
Himachal Pradesh reported its first two cases
March 22^nd 2020
India observed a 14-hour long curfew (Janta Curfew) both to try and combat the coronavirus pandemic and assess the country’s ability to fight the virus. It could also be considered as a trial before actual lockdown could be announced
March 24^th 2020
Prime Minister Narendra Modi announced a total lockdown, effective from midnight on 25 March (Lockdown 1.0)

April 14^th 2020
Nationwide Lockdown till 3 May, with a conditional relaxation from 20 April for the areas that have been able to contain the spread (Lockdown 2.0)