The grandmother of all information sources for adoption from India is IChild. That's where I've gotten most of my information for this blog post.

As with all other international adoptions, the prospective adoptive parents will first complete a homestudy, apply for the I-600A, and complete a dossier for the Indian government. You must use an agency to adopt from India; they partner with an agency in India who will locate a child for referral.

Once you receive your referral then you will have several more months' wait. This is from the IChild website and it explains what goes on in India after you've accepted your referral:

The dossier and supporting documents from your agency are sent to CARA (Central Adoption Resource Agency), the national governmental agency responsible for overseeing adoption. Agencies in West Bengal (i.e. Calcutta) are exempt from this requirement.
CARA approval can take 1-6 months, depending on timing, how well your dossier is structured and your agency’s goodwill at CARA. Upon approval, it is forwarded to the Indian Agency.

The agency must clear your child through the local VCA (Voluntary Coordinating Agency - made up of all the adoption agencies in the area).

A government social worker must visit the nursery and your child to confirm the conditions and his or her health. The social worker must submit a report to the court based on his or her findings before the first hearing. The social worker usually has 10 days to accomplish this review and submission.

There are usually three court dates. They are typically held 10 days apart, although this varies region by region. It depends on the pace of the family courts or the high courts (different courts handle adoptions in different areas). The time necessary for the court's consideration of your case will vary depending on local holidays and court recesses (some close for the entire summer, others close for two weeks at Christmas etc).

At the first one, the attorney representing the agency submits your application to adopt (gain 'guardianship') your child to the courts. It must include the CARA, social worker’s and VCA clearance documents. At the second court date, the documents are reviewed in court. On the third court date, the final hearing occurs where the judge makes the ruling that you shall be granted guardianship. A few days later (or immediately, in some courts), the judge makes a proclamation in open court (dictating the guardianship papers) granting your guardianship of your child. The issuance of a court order document may take 0-6 weeks. Some courts are computerized while others are in the dark ages with antiquated type-writers.

The original court order is forwarded to your Sponsoring Agency Coordinator. S/he will send you a copy of the court order and proceed with the next step.

The Indian Agency will use the court order to process you child’s Indian passport on an expedited basis. This usually takes between five and ten working days.

Go to part 2.