I've been helping someone start their business in India, so I can give you some info.
Your company should be incorporated in the US. You get tax rebates (not available to Indian companies) if you pay for services in USD from a foreign account. Typically you'll pay a local company directly and they will pay your workers (something like a ghetto version of Ambrose Employer Group in the US). Labor is cheap, but often of low quality. Lying on resumes is rampant, and filtering the wheat from the chaff is very tough. Getting good people can be tough for a startup, most people will want to work for bigger company [1]. Pay can be considerably higher in bigger cities. Bombay is more expensive to live in than NYC, and pay can be comparable for great people (though the spread is much wider than NYC). If you need top talent, go to the Valley. If you need commodity talent, go to India.
(I'm not saying top talent doesn't exist there, I'm just saying you probably won't find it.)
Often you can get a package deal - office, servers, workers with a single payment. The SLA will usually have terms like "you don't have to pay workers while the servers are down." My friend exercised this clause several time - between power loss, workers tripping over wires, broken DSL (!!!) connection and the like, he has about one 9 of uptime. Just accept it, plan for outages (read: no MongoDB) and move on. Production servers live on linode/EC2/rackspace, not locally.
You want to avoid a permanent presence - if you can't easily walk away you are at risk of being shaken down for bribes. "Sorry, but the electricity is down, and it will take 2 years to fix it, though maybe I could do a personal favor for you and push you further up the queue." Same thing if you need permits, want to incorporate locally, etc.
Short version: living is cheaper (not as cheap as you think), commodity talent is cheap, but quality will often be lower. Look for bargains, and be aware that it isn't the valley or NYC.
[1] This is true for both cultural and economic reasons. Short version: a) working for an unknown company can mess up your prospects in arranged marriage market, b) family might be disappointed, which is a big deal and c) risks are a LOT higher so stability is valued.
On c), in India, you have a LONG way to fall. Utter destitution in the USA (i.e., bottom 5%) is roughly comparable to upper middle class status (top 95%) of India, in terms of PPP-adjusted income. http://economix.blogs.nytimes.com/2011/01/31/the-haves-and-t...