"Law" is actually a very broad term, which encompasses statutes, rules, regulations, precedent and I'm sure some other things that I'm forgetting. The popular understanding of "law" is the statute, which involves Congress (at the federal level) or the legislature (and the state level). That is the kind of law that we say is "passed". At the federal level, some number of representatives or senators will introduce a bill into the House or Senate, and it is discussed in a relevant committee; if it is approved, it moves to debate by the whole House / Senate and if it passes it moves to the other house. Once it has passed both the House and Senate, it goes to the President where it may be signed, rejected, or ignored. If signed, it becomes "a law", if rejected (vetoed) it can become law anyhow if it gains a 2/3 majority vote in both houses. If the President ignores it ("pocket veto"), it becomes law in 10 days (Sunday is not a day), unless Congress is not in session. Oh, and, that's just the tip of the iceberg.
At the state level, there is a similar process, with the further option of referenda and initiatives. In the former case, a particular law will have been passed by the legislature and then it is put to a popular vote for affirmation / overturning, and in the latter case a new law is proposed by the people (generally through a petitioning process) and then voted on by the populace. There is a fair amount of variation on how this works and what can be done, by state.
A law can be repealed (withdrawn) by passing a law that repeals a given part of the existing law, and it can be re-written. The Supreme Court of the jurisdiction can also withdraw a (part of a) law if it is found to be unconstitutional. No foreign body can override US law, although if the US is bound by treaty (which necessarily involves another country) then we might have to do whatever that treaty says, because we approved the treaty. One limit on what we can be forced into by treaties is that a treaty cannot violate the constitution.
The largest source of law in the US is actually not statutory, it is regulatory law, where a regulatory agency writes rules with the force of law (so really, it is law). In that case, there has to be a statutory basis, where at the federal level a law is passed empowering an agency to write rules, where the scope of the regulation is supposed to be related to the empowering statute in some manner. In that case, there is a vetting process, but basically no voting, just an announcement, some discussion, and eventually the rules are set. Analogous processes exist at the state level.
We also have various county and city governmental bodies, where e.g. the city council can vote to create a law; or, they can empower an agency to write regulations.
Yet another source of law is the Executive Order, where the president can decree that such and such will be the case (as long as it has something to do with what the executive branch does). These are somewhat limited in scope, but every president seems to like to test what that limit is. Governors get to do it too!
And lastly, courts have an indirect power to make law, by ruling on how an existing law is to be interpreted (as well as ruling that a law or part of a law is unconstitutional).