1. Take your total worldwide net worth at fair market value as if all your assets were sold the day before your expatriation date.
2. Subtract your total worldwide cost basis from your net worth. The result is your total gain from your mark-to-market "deemed sale."
3. Subtract $690,000 (tax year 2015, adjusted annually for inflation) from your total gain. The result is your total taxable gain. If your total taxable gain is zero or negative, stop: you do not owe any Expatriation Tax.
4. Otherwise, pay ordinary capital gains tax rates on your total taxable gain, with a current top marginal tax rate of 23.8% (if the NIIT applies, and I'm not sure it does, but let's assume that). This is your total U.S. Expatriation Tax.
If you owe Expatriation Tax your cost basis is reset. Any subsequent capital gains on U.S. assets will only be taxed based on your new, reset cost basis. Note that "wash sale" rules do not apply when making the Expatriation Tax calculation, so deemed sale capital losses are not limited within the calculation. To some degree you can pay your Expatriation Tax in installments if you wish and only pay statutory interest on deferred payments (currently 3%). If your assets are generating a higher after-tax rate of return (quite likely) then stretching out your Expatriation Tax payment to the maximum extent allowed by law is a good idea. You may also wish to stretch out your Expatriation Tax payments if you prefer to raise funds more slowly, perhaps as in the form of interest, dividends, royalties, and/or earned income.
The U.S. Expatriation Tax is not a hardship by any reasonable definition of hardship, and it's quite disingenuous to complain about not getting a $250,000 capital gains exclusion on a home when you're getting a $690,000 blanket exclusion. But if it were a hardship, there's a simple, 100% effective solution to avoid the U.S. Expatriation Tax: don't renounce or relinquish U.S. citizenship.