If you ever resided in the USA, you need to contact the state where you last resided.

If you never resided in the USA, then this would depends on where your parents resided. This page describes the rules in details for those who never resided in the USA. I have reproduced them below. Process and rules varies from state to state. Some states are missing in the list below.

In some States, U.S. citizens, 18 years or older, who were born abroad but have never resided in the United States, are eligible to vote absentee. The following States allow these citizens to vote absentee:

Alaska. A U.S. citizen who has never resided in the U.S. and whose parents were last domiciled in Alaska is eligible to register to vote as a "Federal voter" and may vote in Alaska.

Arizona. A U.S. citizen who has never resided in the U.S. and whose parent is qualified to vote in Arizona is eligible to register to vote and may vote in Arizona.

California. A U.S. citizen who was born abroad, who is eligible to vote, and who has not previously registered to vote in any other State, may register and vote in the California county where a parent or legal guardian would be eligible to register and vote.

Colorado. A U.S. Citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the county where a parent would be eligible to register and vote.

Connecticut. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the town or city in Connecticut where a parent or legal guardian would be eligible to register and vote.

Delaware. A U.S. Citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the county where a parent would be eligible to register and vote (for Federal offices only).

District of Columbia. A U.S. citizen born abroad who is eligible to vote and has never lived in the U.S. and is not registered to vote anywhere else in the U.S. is eligible to vote at the same voting residence in the District where a parent or guardian would be eligible to register and vote.

Georgia. If a U.S. citizen outside of the U.S. has never lived in the U.S. and either parent is a qualified Georgia voter then, that person is eligible to register and vote where his or her parent is a qualified voter.

Hawaii. A U.S. citizen who has never resided in the U.S. but has a parent who is eligible to vote in Hawaii is eligible to vote at the same voting residence claimed by their parent (for local, state and Federal office ballots).

Illinois. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the county where a parent would be eligible to register and vote. Use the most recent residential address in Illinois of a family member.

Iowa. If a U.S. citizen outside the U.S. has never lived in the U.S. and either parent is a qualified Iowa voter then, that person is eligible to register and vote where his or her parent is a qualified voter.

Kansas. Please contact your local election official to determine if you qualify.

Kentucky. For the 2014 General Election, a U.S. citizen born outside the U.S., who is eligible to vote and who has never lived in the U.S. may register and vote where the parent would be eligible to register and vote in the Commonwealth of Kentucky.

Maine. A U.S. citizen who has never lived in the U.S., but who has a parent who is a qualified elector in Maine, may register and vote at the address where that parent is a qualified elector.

Massachusetts. A U.S. citizen who has never resided in the U.S., but has a parent who is eligible to vote in Massachusetts is eligible to vote at the same voting residence claimed by their parent for Federal, State and local.

Michigan. An eligible family member of an overseas voter who is a citizen of the U.S., is accompanying that overseas voter, and is not a qualified and registered elector anywhere else in another State or territory, may apply for an absent voter ballot even though the spouse or dependent is not a qualified elector of a city or township of Michigan.

Nebraska. A U.S. citizen 18 years or older who has never resided in the U.S., but has a parent who is eligible to vote in Nebraska, and has not registered to vote in any other State of the U.S., is eligible to register to vote in one county in which either of their parents claimed residence (for local, state and Federal office ballots). The citizen must include with the registration a signed form provided by the Nebraska Election Commissioner or County Clerk.

New Hampshire. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the town or city in New Hampshire where a parent or legal guardian would be eligible to register and vote for Federal offices only.

New York. A U.S. Citizen who was born abroad and who is eligible to vote and who has never lived in the US may register and vote in the county where a parent would be eligible to register and vote (for Federal offices only).

North Carolina. A U.S. citizen who was born abroad and has never lived in the U.S. may register and vote in the North Carolina county where a parent would be eligible to register and vote.

North Dakota. A U.S. citizen, who was born abroad, has never lived in the U.S. and who is eligible to vote, may vote in the county where a parent is eligible to vote.

Ohio. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the town or city in Ohio where a parent or legal guardian would be eligible to register and vote.

Oklahoma. A U.S. citizen, outside the U.S., has never lived in the U.S., and either parent is a qualified Oklahoma voter, then that person is is eligible to register and vote where his or her parent is a qualified voter.

Rhode Island. A U.S. citizen who has never lived in the U.S., but has a parent who is a qualified Rhode Island elector then, that person is eligible to register and vote in Federal elections.

South Dakota. Any overseas citizen may register and vote in any Federal, State, county, or local election held within South Dakota under the following condition: (1) The overseas citizen, or the spouse or parent of the overseas citizen, was last domiciled in South Dakota immediately prior to departure from the United States (2) an adult child of the overseas citizen has not reached the age of 22.

Tennessee. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register temporarily and vote in the county where a parent would be eligible to temporarily register and vote pursuant to this action.

Virginia. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the city or county where a parent would be eligible to register and vote. However, your eligibility to vote may be restricted to Federal elections, please contact your local registrar for additional information.

Washington. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the county where a parent would be eligible to register and vote. Use the most recent residential address in Washington of a family member.

West Virginia. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the county where either parent would be eligible to register and vote.

Wisconsin. A U.S. citizen who was born abroad and who is eligible to vote and who has never lived in the U.S. may register and vote in the in the city or village where a parent would be eligible to register and vote (for Federal offices only).

Wyoming. A U.S. citizen who has never resided in the U.S. and whose parent(s) is/are qualified to vote in Wyoming is eligible to register to vote and may vote in Wyoming.