This is pretty straightforward, there are two main ways that an existing US state (or a part of one) might secede from the US.

One would be a constitutional amendment that created a new process that would allow for that to happen (which is effectively identical to secession through mutual consent of the seceding state and the remainder of the states). In 1869 the US Supreme Court decided in Texas vs. White that Texas did not have the right to unilaterally secede from the union:

The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.

You'll note that leaves open the gap for a mutually consensual secession, as mentioned above. It's questionable how that would work in practice as there is no precedent for it. One certain way it could work is by amending the constitution to create a formal process. Potentially something like congress and the senate agreeing (passing a bill or resolution) to allowing a particular state to secede might be possible given the ruling from Texas vs. White. However, nobody really knows what that would look like. One weirdness is that theoretically the seceded state would still be subject to the US Constitution, they would just become basically a new "United States" (e.g. US-prime or US v. 2 or 2 United 2 States, or whatever) with their own congress, president, "federal" government, etc. Though it would be much easier for them to change that, of course.

More realistically, the process would occur extra-legally, through revolution, perhaps violent perhaps bloodless. A state would just declare itself not part of the US anymore (as many states did in the 1860s), and instead of being brought back into the union they would stay independent. That's how laws work sometimes, by being broken and by people building new systems of laws on new foundations while abandoning the old ones.

Currently no state has successfully seceded from the US so far, so trying to imagine how it would happen in reality is mostly speculative.