Thing is I am in a dilemma on how should I approach my employer?
Bring it up with your manager during your next 1-on-1 meeting.
Instead of asking for a 1-month vacation now, just ask about the company policy for such vacations instead. As Monica Cellio points out, you could ask in an open-ended way -- not "I'd like to take next month off" but more like "sometime in the next {several months, year, whatever - but not immediate} I'd like to take a few weeks to visit my family in India; how do we handle longer leaves?" This is something anyone wishing to travel home for long periods of time will need to know.
Any US company that regularly hires folks from India, China, etc. has already faced this sort of issue, and will likely already have a protocol in place. That is certainly the case for my company. We regularly arrange such lengthy vacations, although requesting one when you have been at the company for only two months wouldn't usually be acceptable in my company.
Many companies would expect you to wait until you have actually accrued 4 weeks or so worth of vacation time. If that is the case at your company, HR would be able to tell you how your vacation accruals work, and at what point you will have accrued 4 weeks vacation.
Some companies will permit you to "borrow" unaccrued vacation time. Again, HR could tell you.
A few companies will not permit you to take more than a few weeks vacation at a time.
As David K points out, you could also ask about the possibility of working remotely, if the job and the trip allow it. Answering emails and getting some work done could certainly ease having someone away for a month.
It may depend on your role within the company, what is going on at the moment regarding projects, who can replace you for a month, etc.
But in almost all circumstances, it will be necessary to work with your manager when requesting your vacation. Your manager will need to coordinate your schedule against your projects, and whoever will fill in for your work in your absence.
In my company, most folks wishing to travel back to India save up their vacation time, and travel once every two years at most. On some occasions (emergencies) we allow folks to "borrow" vacation time. In some cases, folks bring a computer with them to work remotely.
Your mileage may vary.