On October 31, the House voted to approve a formal resolution outlying the terms and parameters of its inquiry, but is still in the fact-finding stage of the process, hearing witness testimony and reviewing documents related to the inquiry.
The impeachment process begins in the House Judiciary Committee, which draws up articles of impeachment based on the results of the inquiry.
The House hasn't yet determined whether they'll limit the scope of the inquiry to the allegations raised in the whistleblower complaint and corroborated by administration officials, or if they'll include articles related to obstruction of congressional investigations.
If the committee passes the articles of impeachment by a majority, they go to the full floor of the House of Representatives and require a simple majority vote of 218 members to pass. Members vote on each article individually, meaning Trump could be impeached on some articles but not others.
Former President Bill Clinton, for example, was impeached on articles of perjury to a grand jury and obstruction of justice, but he was cleared on a separate perjury-related article and a charge of abusing his office. In January of 1999, the US Senate acquitted Clinton on both charges.
In order for Trump to be removed from office, two-thirds of the US Senate — 67 members — have to vote to convict him of those articles of impeachment. Currently, the Senate consists of 53 Republicans, 45 Democrats, and two independents who caucus with Democrats.
If Trump is not impeached at all or impeached but not convicted in the Senate, he stays in office and it'll be left up to the American people to either re-elect him, or vote him out of office in 2020.