Amazon is boasting that the Indian Kindle Store features a vast selection of ebooks from a range of Indian authors, including Chetan Bhagat, Ashwin Sanghi, Ravinder Singh and Amish Tripathi. They also have gone the usual route with exclusives; readers will also find exclusive Kindle ebooks such as Reality Bites; a not so innocent Love Story by Anurag Anand, Love, Life and a Beer Can by Prashant Sharma, as well as over all the free classics that you've come to expect in an ebookstore.
Indian readers can also buy a Kindle at any one of 70 odd Croma stores. Amazon has signed up the electronics chain as their first Indian retailer. The Kindle apps are also available to Indian readers, but note that the Kindle Fire is not.
You can also find the Kindle via the Junglee, Amazon's Indian sub. Junglee is a 3rd party retailer marketplace which operates much like Amazon, with the exception that Junglee doesn't handle any of the goods. This is likely the company that Amazon will rename as Amazon India when they officially launch in the republic.
I'm in the mood to puncture balloons, so I'd like to point out that there is a notable lack of ebooks in any of India's languages besides English. In spite of what you might think from meeting Indian expats (or talking to Dell's tech support), the official language of India is Hindi, with English adopted mainly because of the dominance of Britain in colonial times and then the US now. Furthermore, India has over 1500 languages as well as 30 languages which each have over a million native speakers. You cannot buy Kindle ebooks in those languages, either.
The reason I'm pointing out the language issue is that this launch more of a flub than a milestone. One might as well launch an English-only ebookstore in Europe and be thrilled that you covered a market with 500 million consumers.
But Amazon's mistake is also good news for their local competition. India has a population of 1.2 billion, including some rather large language concentrations. Truly supporting that market is going to require support for more fonts, scripts, and languages that Amazon is wont to do, and that means there is an excellent opportunity for someone to jump in and take it away from them.