Designated competent authority(ies) to issue an apostille in India:

Ministry of External Affairs of the Government of India

There are two ways of doing an apostille in India

a) Get the state attestation then MEA apostille
b) Get MEA apostille skipping state attestation

A- with state attestation

This is a safe way but more elaborate way where you have to go to state govt who issued this document submit your documents there and pay a nominal fee get your documents state attested.

But above explanation makes you feel the state attestation easy but in really it is totally different.Since state govt are slow like a snail you it will take months together to get the state govt attestation.

For birth certificate state attestation following is the procedure

Go to secretariat of your district submit the documents pay a nominal fee 
after getting the permission from Secretariat take your original documents to birth certificate issed authority such as municipal in your locality. Get a seal from them, take this sealed original documents to Secretariat again get the state attestation seal from them.

Now its time for MEA apostille

To get MEA apostille you cannot directly go to mea just like you went to state authority. You must go to any certified agent and get your documents apostille.

It will take 3–4 days or 1 week or 2 week depending on the charges you pay.

I would suggest make a informed decisions before handling to any other agent once you submitt the documents they will have control over you so I recommend you to search on google maps and go with the agents who have hieghest ratings and feedback, so you will be more informed on with whome you should go.

b)Get MEA apostille skipping state attestation

The procedure for getting Apostille without state attestation is as same as getting MEA apostille after getting state attestation. You give the documents to agents and they will get it done for you.