Each state makes its own laws about who can vote in elections and run for office as well. As you may note, I have some legal training. Therefore I prefer we start with the common definition of our venture. We agree that USA.GOV is a website operated by the United States Government.
At the link above, you search for your US state’s department of elections website. When you find your state’s link, search for ‘Register to Vote.’
You may be forwarded to your county’s website, where you will follow their instructions.