I'm looking to hire a full time programmer in India. Of course he would need to pay tax in India. But would I also need to pay tax in USA? If I've got an LLC taxed as an S-Corp in California?
There are no tax implication for you in the US other than with any other business expense. Since the developer will most likely be R&D or capital expense, this will reduce your overall taxable income because you are using the developer to build your business.
You only pay taxes in the US for the income you generate. Having expenses reduces your income so you pay less taxes.
Sites to recruit developers: There are many freelance/project listing websites, e.g. odesk.com, elance.com or freelancer.com, that let you use your credit card to pay the developers on an hourly basis. These sites also have feature