who has the power to begin the process of impeachment

In the US system, it's actually the House of Representatives that gets the ball rolling on impeachment. They hold the sole power to formally charge a federal official with misconduct. It's not like just anyone can walk in and start the process; it usually begins with someone introducing a resolution, which then has to go through the committee process before the whole House votes on it.

Once the House votes by a simple majority to impeach, the whole thing moves over to the Senate. That's where the actual trial happens. I remember watching some of these proceedings on the news over the years, and it's pretty intense how it shifts from the House being the ones to bring the charges to the Senate acting as the jury. It's a long and complicated road for sure, but that's how the constitution set it up to keep things in check.