The magic form you need to remember is Form 2555. This is the "foreign earned income exclusion" form. The first "close to $100,000" (the amount changes annually for inflation) of income you earn abroad is free of income tax in the USA.
The hard part is knowing whether you qualify for this or not. You need to be physically out of the USA for 330/365 days in a 12 month period (not a calendar year--this is stupidly overly complicated and tricky), or be a "bona fide resident" of the other country. Look at the instructions on the form to help you here. Most people fail on this point, and this is the first vector of attack by the government to try and tax you.
CAUTION CAUTION CAUTION. I see any number of Americans abroad who work as self-employed independent contractors. Oh, hypothetically, software engineers living in Thailand and working. They successfully spend 330 days out of the USA. They use Form 2555 to eliminate income tax on their Schedule C self-employment income.
But Form 2555 _does_ _not_ _eliminate_ the self-employment tax -- the equivalent of Social Security tax for self-employed people. See Schedule SE.
Sorry for using all caps and fakey-fake underlining to emphasize this problem. It happens all the time. I saw it yesterday. You think you have no tax liability and you end up owing $16,000 for self-employment tax. Not fun. At all.
The next magic form to remember is Form 1116. This is the foreign tax credit. If you earn a dollar of income in Japan and pay Japanese income tax on it, Uncle Sam will give you credit on your U.S. tax return for the Japanese income tax you paid.
This is usually the better way for Americans abroad to go when they live in high-tax countries. This is why Americans in Europe pay many thousands of dollars to have a tax return prepared but never give Uncle Sam a nickel of tax.
If you are an American abroad working for a foreign employer, you don't have to pay U.S. Social Security. You should look at the totalization agreement between the USA and Japan to see if you can eliminate the need to contribute to the Japanese old age pension schemes since you aren't going to retire and die in Japan.