Where to pay taxes if you have dual citizenship in the US and Germany?

The US does not officially recognize "Dual Citizenship." That doesn't mean it's illegal or anything, just that they don't care: if you are a US citizen, then you pay US income tax, regardless of whether or not you are a citizen of some other country as well.

I don't know what the German rules are, but it's at least possible you could have to pay income tax to both.

If you're living in one country and could theoretically claim citizenship in the other but haven't done so yet, as far as taxes are concerned you could be better off just ignoring your potential citizenship.

If you're living in Germany, the US does have treaties with some countries which allow US citizens living abroad to deduct taxes paid to those countries from their income for US tax purposes, at least partly. You should contact the IRS for their publications on tax treaties and citizens living abroad (publications 54 and 901, I believe).