Reporting capital gains on foreign income...how to claim tax credit?

If you exercise stock options in a same day sale in a US company, the US company should withhold social security, medicare, federal, and state taxes on your profit. And they should send you a W-2 with wage income = to your profit plus your normal salary minus deductions. This goes on line 7 of your 1040. But there may be a tax treaty to exempt the withholding of some or all taxes.

When you exercised your US stock options, was any money withheld in taxes?

I'm not sure if the stock option profit qualifies from the foreign earned income exclusion. But it will qualify for the credit, as long as you paid taxes to Germany for it. You claim the credit by filling out form 1116.

If Germany has taxed the same income that the US has taxed, then you will need to complete Form 1116 to calculate the foreign tax credit. Please note, that this form is not for the faint-hearted under any circumstance. It can be especially complex when dealing with qualified stock options (you did say ESPP) that have both a compensation component and capital gain/loss component. I recommend you see a tax pro to complete it.

If you are not discussing a large or significant amount of money, you could elect to take a tax deduction (see Form 1040 Schedule A Line 8 if you itemize) for foreign taxes paid rather than a credit. If you make this election, you must use the deduction method for all foreign taxes paid in that tax year.