First, according to the statements and writings of the people who actually wrote the relevant part of the Constitution, the Constitution never had "birthright citizenship". That was a clear misinterpretation forced on us many decades ago by an incompetent Supreme Court. None of this involves getting rid of a Constitutionally provided power. It's removing from the government a power that it never properly had.

Second, it would work as it works with almost every other nation on Earth: citizenship would derive from parentage, and naturalization (there are a few exotic exceptions, but that's almost all of it).

These are, roughly, the criteria that are used by most nations, and would probably be used here:

1. If one of your parents was a legal American citizen at the time that you were conceived, or was naturalized by the time of your birth, then you have a claim to citizenship.

2. If you came to America legally, on the proper visa, and successfully completed the legal process to become a citizen, then you have a claim to citizenship.

3. Otherwise, you have no claim to citizenship.

That's it. That's more or less the way that almost every nation on Earth does it, and has done it for a long time.

For decades, America has had some of the broadest criteria on Earth for becoming a citizen, just as we've measurably (and measured, and the results of said measurements published in the peer-reviewed literature) had almost the highest level of "diversity", and the lowest level of racism, among nations.

Liberals have continually lied about that, because if Americans knew that, then most of said liberals' emotional appeals for liberal immigration policies, which are almost entirely dependent on invoking guilt in the listener, would fail. Which Americans would feel guilty about too little diversity, or too much racism, if they knew that America had long had more diversity, and less racism, than almost any other nation on Earth?