Did this ever explain how Godzilla was resurrected?

TL;DR: Both the Japanese and American versions of the movie simply dodge this issue.

In the Japanese version, it is implied - though not stated - that this is another kaiju of the same species, a la Godzilla Raids Again. We are told only that this Godzilla was lying dormant beneath an island within the Izu chain and awoken during the volcanic eruption that is seen during the opening credits sequence. The fact that he's 80 meters tall (30 meters taller than the first Godzilla) would suggest that he's another, larger (and possibly older) animal. But what's confusing is that everyone in the movie still talks about Godzilla as though he is the only creature of his species that has ever existed.

The American version simply ignores the existence of the oxygen destroyer and states outright that this is the same Godzilla from 1954. When Raymond Burr is at the Pentagon and the General asks him how Godzilla was killed 30 years ago, he tells the General that, "30 years ago, they never found any corpse."

This movie outright dodges the issue of how Godzilla came back or if he is another Godzilla. The American version implies that it is the same Godzilla, but the Japanese version never even brings the issue up.

In order to learn the true answer, you'd have to watch the rest of the Heisei series, namely Godzilla vs. King Ghidorah and Godzilla vs. Destoroyah. These films establish that the Godzilla that appears in this movie is the result of time travelers moving a dinosaur from the Marshall Islands to the Bering Sea before it could be exposed to the H-bomb test and become Godzilla, only for it to become Godzilla in the first place after being exposed to a Russian nuclear submarine crash in the 1970's. It is later established that this Godzilla is a separate individual from the Godzilla from 1954, which was killed by the Oxygen Destroyer.