I received ISO options in the past. (granted more than 2 years from now)
I exercised the ISO options in the past (exercised more than 1 year from now)
When I exercised, I did the AMT calculation and I did not owe anything.
Today, I am selling the shares from the ISO options. From what I understood, I will simply pay capital gains on the gain of the sale.
When do I pay taxes on the sale?
Do I need to make a payment to the IRS now or at the end of the year when I calculate my overall taxes?
"Do I need to make a payment to the IRS now or at the end of the year when I calculate my overall taxes?"
First off - and this may be something you already know - the fact that the shares you sold were acquired via an ISO is absolutely irrelevant here. It's a simple sale of plain-vanilla "stock", a stock that's no different than a stock that you bought through your broker.
This is one of those questions where to be absolutely correct with an answer we would need to know a great amount of detail about your personal situation, tax-wise. Although the US tax system is a "pay as you go" system which sort of suggests that you should pay the capital gains tax when you incur it, the system really doesn't work that way exactly.
It's perfectly OK to owe the government a lot of money when your tax return is due. What you really want to do is to avoid being "underpaid" (a piece of tax jargon that has a specific legal meaning) and incurring large penalties.
Most taxpayers will avoid being underpaid if they:
1)owe less than $1,000 in tax after subtracting their taxes WITHHELD and available tax credits,
2)if they paid at least the lesser of
a)90% of the tax for the current year, or
b)100% of the tax shown on the return for the prior year. (If last year's return shows AGI over $150K (for married filing jointly) then change that "100%" figure to "110%.)
So if you're still working, still having taxes withheld, maybe even more taxes than you had withheld last year because of salary increases, then you probably don't need to pay any estimated taxes. ("Estimated taxes" are taxes you pay directly to the IRS out of your own pocket because there's no withheld taxes on your income, e.g., you're an independent contractor or you have significant income from other sources like dividends or capital gains where taxes are not withheld automatically.)
The 2)b) "safe harbor" noted above is certainly the easiest to figure out, so pull out your 2018 income tax return, look at the 2018 total tax liability figure, (that's line 15 for most people, though Pub 505 does spell this out in more detail). If your projected withholding gets you into this safe harbor to avoid being underpaid, or you can increase your withholding to get you there, then there's no need to pay anything now.
If you want a more precise answer then go to the "Form W-4 and estimated taxes" interview in TurboTax and work through the "Review your estimates" interview. That's where you'll make your best guesses as to 2019 will look like when you file that income tax return.