Well there are two different ways. One involves a fiancé visa that once approved allows you to travel to the US where you get married and file all papers there. The other process involves filing papers after your marriage and while you wait in India for approval. Either process can take a year or two before completed.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
The process differs if you are in the US or outside of the US. Generally, once married your husband must file a family based petition on your behalf. That is but the first step. After that you are either adjusting status or applying for a visa. Please contact a US attorney for specifics in relation to your set of facts. If you are outside of the US you can have a Skype consultation with an attorney.
Retain a reputable immigration attorney for the best results.
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If you are outside the U.S., your spouse files an I-130 visa petition for you. Ultimately it will be sent to India for you to get the visa and be admitted to the U.S. Takes about one year or more.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
While arranged marriages are common among Indian couples, you face a unique challenge in proving good faith due to the short 'courting' period. Nevertheless, it is certainly doable with the help of an immigration attorney familiar with the issues. I highly suggest your fiancé, if he's in the US, contact an immigration attorney for a consultation. Best of luck!
Dhenu Savla, Esq.
This answer does not create an attorney-client relationship and is not meant to be relied upon as legal advice.