Hi Amax - do you have a particular investment objective in mind? Is this just a means to have a stake in the Indian stock market in general (and benefit from its rise etc) or targeted at specific companies whose shares you wish to own?
A handful of large Indian companies have ADRs (American Depositary Receipt) - which you could purchase directly through your e-Trade account. See Adr.com - the India page is at http://www.adr.com/adr?page=region&formtype=6&country=IN.
There are mutual funds and ETFs that can give broad exposure to the Indian market - e.g. closed ended funds such as IFN or IIF. Some more vehicles detailed at http://www.parchayi.net/invest.php. All these would be purchasable through your eTrade account.
The Indian stock market is prone to volatility. Also India has let its currency appreciate, which can heavily impact many Indian companies that depend on exports (though the Indian market as a whole is driven more by internal demand than exports). On the flipside, it helps to control inflation for imported commodities (of which they will need record-breaking amounts in the coming years to sustain their growth).
You should have a stomach for risk when you invest in this market. This paper from the World Economic Forum is worth reading to get a perspective on the risks: [broken link removed].