The US is one of very few countries in the world that taxes their citizens who live abroad.
So yes, technically you'd be subject to pay income tax in both the US and the country you live in, but it is likely that there is a tax treaty with the host country that will let you deduct any local income taxes paid from your US taxes.
In practice, this means that you will pay only one income tax (but file two returns).
You do not have to pay income tax if you spend less than 30 days in the US that calendar year. You do have to pay any self-employment tax, however. The rules are extremely complex and I highly advise consulting someone who understands them.
You do not have to pay income tax if you spend less than 30 days in the US that calendar year.
Careful with tax advice from the Internet, folks. idlewords is talking about passing the Physical Presence Test for the Foreign Earned Income Exemption. If you quality for the FEIE via either the physical presence test or the bona-fide residence test (see the IRS docs, they are fairly easy to understand), you get to exempt the first X of your income from the income tax. X is in the $80k range this year, check your friendly local IRS website.
Regardless of the FEIE, your income is not exempt from self-employment taxes, as idlewords said. Additionally, it has to be EARNED income, a distinction which has VERY IMPORTANT CONSEQUENCES for people here who are intending to sell their startup at some point. To oversimplify, earned income is the portion of your profit you gain in return for services rendered, but it excludes the return on invested capital -- including IP. So if you end up selling your business for $500,000, it is highly likely that large portions of that are not earned income, and will be taxed from the first dollar in the US.
Taxes are a minor headache for me every year, and this year my business gets to start filing with Japan, too. Yaaaaaay, more fun.
As far as I can tell - having moved to Austria and acquired a tax specialist - this is backwards.
The US gets first dibs. At least they do in my situation. Then the full amount I pay to the US in tax (100%) is removed from the taxes I owe in Austria.
Simple example: Austria says I owe 20,000 euros. US says I owe $15,000. I pay the US $15,000. My tax burden in Austria is now approximately 20,000 - 10,000 euros (ballpark currency exchange) = 10,000. (This is assuming you crest theearned income waiver for expats, which is about $85,000 USD now.)
Basically, though, you have to hire a tax specialist. There's no way to manage it simply. And tax specialists with international experience are hard to find, but if you're coming from the US you'll have an easier time than if you're coming from a smaller country. Your best bet would be to contact one of the larger international firms, e.g. Deloit. I had to search for 9 mos to find one, myself.
(As an aside, I'm outraged that I have to pay US taxes at all.)
So yes, technically you'd be subject to pay income tax in both the US and the country you live in, but it is likely that there is a tax treaty with the host country that will let you deduct any local income taxes paid from your US taxes.
In practice, this means that you will pay only one income tax (but file two returns).