I thought I remembered reading somewhere that there was a separate form that expats could fill out.
Check out Form 2555 (foreign earned income exclusion) and Form 1116 (foreign tax credit). Both of these are discussed at great length on this board and elsewhere. Tax software can help you fill them in correctly.
Do I pay state taxes?
Each state has its own tax laws, but normally if you're classed as a nonresident you'll pay state taxes only on income from sources within that state. As an example, if you own a house in NY and rent it out, you would probably have to pay NY state tax on the rental income.
However, some states tax based on domicile rather than residence (MA and VA are two examples, but probably not the only ones). If you have ever lived in one of these states you may need to be prepared to show that your domicile is elsewhere - meaning you have cut all your ties with that state. I think there are some very old reports from MA and VA taxpayers on this board.
Also be aware that as a US citizen overseas, federal law provides you the right to register to vote using the last address where you lived in the US and to vote in federal elections (that's for President, House and Senate). Voting in these elections cannot affect your state tax liability. However, if you choose to also vote in state-level elections, a state can use this choice as evidence that you are a state resident and can choose to tax you on that basis. To be safe, you should register to vote here
https://www.votefromabroad.org/ and when prompted, indicate that you are abroad
indefinitely. Your state elections office will then send you a special ballot for federal elections only.
