I am a U.S. Citizen, how do I apply for a green card for my Indian spouse?

It depends on the situation. If your husband is in the United States now on a visitor's visa then you can simply file a petition for adjustment of status. If he is not in the country now you will have to file an immigrant visa petition for him using Form I-130. We have a guide that tells you how to do this.

If he is in the country, you can follow the steps for adjustment of status in the fiance visa guide here.

You can only apply at the consulate in India if you have been a resident of India for at least 6 months. (At least this is the general rule, it varies from post to post so you would have to look at the web page for the specific post that has jurisdiction over your place of residence.)