For the most recent precedents (the Nixon and Clinton impeachment efforts), the House Judiciary Committee took the leading role, holding hearings and gathering witness testimony, and eventually drafting their formal accusations against the president as “articles of impeachment.” The Judiciary Committee then voted to approve those articles and send them on to the full chamber. The Trump impeachment inquiry featured a hybrid process in which the Intelligence Committee did primary fact-finding, wrote a report, and then kicked the report to the Judiciary Committee, which drafted the actual articles of impeachment.
But the endpoint in the House is a vote of the full chamber on each article of impeachment. If even one article is approved by a majority, the president has been (dun dun dun ...) impeached.