Next month (8 November) is the American presidential election. But early voting has already started – early voting in person is allowed in 33 states and early voting by mail is allowed in 27 states (English Wikipedia). And that isn’t even counting absentee ballots for citizens living overseas or in the military.
I am a bit late to the game but this year I decided to register to vote for the first time :). This entails filling out an absentee ballot and sending it back to the county of one’s last official U.S. address. For me, this means sending it to Rockland County, New York as my last American address was in Pearl River, NY. A county is made up of a group of cities that work together under the same administration, and an American state is generally made up of these counties. So state -> counties -> cities.
For voting information, you can visit fvap.gov, or the Federal Voter Assistance Program. They have articles there like 5 things you need to know to vote absentee.
Step 1 is to download the FPCA (Federal Post Card Application) and mail it in to get into their system. You have to do this at least every few years – mine says it expires at the end of 2018. Also in New York you have to declare your party about 5 or 6 months in advance (Democratic or Republication) if you want to vote in the primaries. The primaries were earlier in the year, and are used to determine who will lead the Republication and Democratic tickets. You can read more about it here.
The only drawback at the moment is that New York state hasn’t fully embraced the digital age. So I can download the FPCA from the website, but I need to send it a hard copy (even if I also email it).
Step 2 is waiting for the actual ballot to arrive. Mine arrived last week, and I filled it out and put it in the mail yesterday. Like the FPCA, you need to mail it a hard copy, not just vote online.
Here is a look at what arrived:

The actual ballot is open in the middle. Above that, you have a smaller envelope which you date and sign. You then place the ballot inside. It’s a security envelope, so you can’t look through it. Below, you have a slightly larger envelope which you put the smaller envelope inside. You put your return address in the upper left and (since I am not in the US) appropriate postage to get it back to the US. Postage is only paid for if mailed from within the US.
And a close-up of the actual ballot:

On this ballot, you had three choices: President and Vice President (column 1), US State Senator (column 2), and not pictured, the House representative. The last race featured Nita Lowey, who was running unopposed.
A bit interesting – you can see that the race for President/Vice President had some duplication, as both the Republications and the Green party supported Trump/Pence. Similarly, there was some duplication for Clinton/Kaine (Democrats, Working families, and Women I believe).
This ballot is from Rockland County, NY. The format probably varies with each county, so this isn’t indicative of all ballots. And in a week or two I can check back online to see if my ballot was received and counted.