You register with the election commission (the government) but in order to vote in party primaries, you have to register as their party. You're free to register as an independent.

You either register with the Post Office(USPS) or with your city's/county's/state's government. For California you can see the registration form and options here(just click register and say yes and you'll see the form with options): https://registertovote.ca.gov/

You register to vote and, depending on state/county, you choose what party you belong to(Republican, Democrat, No Party, Green Party, etc.). You may need to register with a specific political party because of open vs. closed primaries where you MUST be a registered Republican to vote in the Republican primary and/or register Democrat to vote in the Democrat primary, etc.

California has a good website/page with more details: https://www.sos.ca.gov/elections/political-parties/no-party-preference/

Again, different states have different ways of doing things.

Registration streamlines voting in that you don't need to bring ID, proof of eligibility, and residency to the polling place. You just show up and they check your signature.

Party declaration determines what party's primary you can vote it. It's to prevent people from casting spoiler votes to help a weak opposition candidate win their primary. Not all states do this: some ask which ballot you want at the polling place.

Those convicted of certain felonies, those diagnosed with certain mental disabilities, non-citizens (such as those with only permanent resident status) and residents of non-incorporated territories (such as Guam and Puerto Rico) cannot vote in federal elections and individual states (and territories) have different potential exclusion criteria.

You have to register yourself to vote, it's not automatic. Some people never register, others are removed from the the registry due to crimes or other things a state might have decided to disqualify someone from voting, though usually that's just a flimsy pretense because the Republicans have a long stories history of just purging minorities/Democrat voters from lists because that will help them win

I mean first of all they want a list so they know you are in fact a citizen over 18 and also that you haven’t already voted.

Also the database includes logistical things like your mailing address for election related mail like mail-in-ballots, and your assigned voting location for states that do that.

Also it includes your party affiliation if you choose to list one so they know which primary you are going to participate in. It’s important to note the system of parties and primaries is somewhat informal because it’s technically not an official legal part of the system, it’s just people with similar political ideas organizing together to get their candidate a better chance.

but can someone from the US please explain me how voting actually works over there?

Gonna simplify a bit here...

There are two main election cycles: the mid-terms and the presidential election.

Presidential elections take place every 4 years in November. 2024, 2028, etc. This also includes a "primary" that starts sometime around March-April, where the candidates for the Democrats and the Republicans are voted for and chosen to then "compete in November. The primary votes are finalized at the respective DNC and RNC conventions.

The mid-terms take place every 4 years, but they are staggered between presidential election cycles. So, last presidential was 2024, so our mid-terms will be 2026. Next presidential is 2028, and the next mid-terms after that is 2030, rinse repeat.

Mid-terms and the presidential cycles are both very important as that is when certain Congressmen are up for election as Senate members are every 6 years and House is every 2 years.

Now, when a US Citizen registers to vote they will have the option to select a "political party preference". This doesn't just mean "Democrat" vs. "Republican", the person can also usually choose from Independent/No-Party-Preference, Green Party, etc. depends on the state. However, there are "closed" and "open" primaries depending on the state and political party. For example, if you are a registered Republican you can vote in the Republican primary but NOT the Democrat one and vice-versa. Some 3rd parties like the Green party can be allowed to vote in the Democrat party primary(open primary) but not the Republican one(closed primary). This is to prevent "sandbagging" or "party raiding", so Democrats can't directly influence Republican primaries and vice-versa. This party affiliation is really only used for primary candidate voting, not for measures or ordinances or anything. Everyone should be able to vote for local laws no matter their political affiliation.

Now, since I'm seeing this a lot on this thread. Your actual votes are NOT tied to your person whatsoever. The ballot we vote on does not have our name on it any other type of identifying markers. Now you can infer that a person registered with the Democratic party probably voted for the Democrat candidate, but the government does not(and practically can't) make a record of who you voted for.

It usually lists known party affiliations and who people voted for that cycle.

It's an extermination list.