I've written about Nixon's impeachment before, and I'll say there were two critical moments. The first took place in October 1973 when Nixon dismissed the independent prosecutor investigating the Watergate scandal. This also resulted in the resignations of the Attorney General and the Deputy Attorney General, the people in charge of the independent prosecutor.
What became known as the Saturday Night Massacre turned a protest movement in favor of impeachment into an actual impeachment hearing. Before Nixon attempted to defuse the investigation, the push for impeachment was largely political. After it, there were enough votes in the House of Representatives to open an impeachment investigation.
The second key moment came in April 1974, after the release of transcripts from Nixon's secret recording system. These transcripts were the key tools that turned most Republicans (some remained with the president even after the end) against Nixon. Newspapers like the Chicago Tribune and writers like William Buckley came out against Nixon or refused to back him up any more.
These transcripts began a push (that ended in the U.S. Supreme Court) to release the tapes themselves. The summer of 1974 was a summer of rising spirit against Nixon, and the impeachment proceedings gained momentum in Congress.
With almost no support for Nixon in Congress, he elected to resign.