The Senate with the Chief Justice of the U.S. Supreme Court presiding, but the President can be tried for impeachment only after articles of impeachment have been presented to it by the House of Representatives, which in effect, functions as a grand jury to bring charges in the first place.
The legislative branch holds the powers of impeachment of the President. The House of Representatives is tasked with bringing forth charges. The Senate is tasked with holding the trial of impeachment.
excecutive
The branch of government that can impeach federal officials is the legislative branch, specifically the United States Congress. The House of Representatives has the sole power of impeachment, which is the formal process of bringing charges against a federal official. If a federal official is impeached by the House of Representatives, the Senate then holds a trial to determine whether to convict and remove the official from office.
Congress may impeach an official from the judicial branch, or the executive branch, for abusing their power. However, the judicial branch holds the trial.
The Executive Branch
the president
The senate holds all impeachment trials. If two thirds of the senate finds him guilty then the president will be removed from office. Only the House can impeach the President, not the entire Congress.
The President of the United States holds the highest office in the US government
Legislative Branch
A simple in the House suffices for the impeachment. The Senate then holds a trial and a 2/3 majority is requited to convict and remove the president from office.
The House Judiciary Committee conducts the formal inquiry into whether the president should be impeached. Based on their findings that recommend to the full house to impeach or not to impeach and submit the Articles of Impeachment ot the full house. The full house debates each article of impeachment and votes on each as to whether or not to impeach the president. If a simple majority votes to impeach the president on any or all of the articles of impeachment, the president will be "impeached." However, it is the senate who tries the president. See related question for more information.
If the President (the Executive Branch of government) wishes to make a high ranking appointment to the executive branch, Congress (the Legislative Branch of government) holds hearings to determine if the appointment meets their satisfaction. After the hearings are concluded Congress votes on the appointment and if it passes then the appointment is "confirmed."