Income that is derived in a foreign country is not taxable provided those funds stay overseas. If you start a business in another country, you can exclude that income provided it stays there. However, you have to report all assets to the IRS. If you do not, there are severe penalties. The IRS has forced banks world wide to hand over the names of US citizens that hold accounts there. Like the article state, the US is the only country in the world that taxes ex pats income that is made in another country.
Ex pats who renounce their citizenship have to have citizenship in another country. This is no simple matter unless you have dual citizenship. It could take you 5 years in a Carribean country to gain citizenship and is a long drawn out process or you can buy citizenship if you are well heeled. Ex pats that are still citizens of this country still have to file and pay federal income taxes on income derived from the states. The renouncement of citizenship has to be filed at a US embassy.
Obamazombie is correct about the length of time you can earn income outside the states without being taxed. I think, you can only come back to the states a couple of times for so many days. Very restrictive.