From the Senate Impeachment Rules:
I. Whensoever the Senate shall receive notice from the House of Representatives that managers are appointed on their part to conduct an impeachment against any person, and are directed to carry articles of impeachment to the Senate, the Secretary of the Senate shall immediately inform the House of Representatives that the Senate is ready to receive the managers for the purpose of exhibiting such articles of impeachment agreeably to said notice.
II. When the managers of an impeachment shall be introduced at the bar of the Senate, and shall signify that they are ready to exhibit articles of impeachment against any person, the presiding officer of the Senate shall direct the Sergeant-at-arms to make proclamation, who shall, after making proclamation, repeat the following words, viz: "All persons are commanded to keep silence, on pain of imprisonment, while the House of Representatives is exhibiting to the Senate of the United States articles of impeachment against ;" after which the articles shall be exhibited, and then the presiding officer of the Senate shall inform the managers that the Senate will take proper order on the subject of the impeachment, of which due notice shall be given to the House of Representatives.
III. Upon such articles being presented to the Senate, the Senate shall, at 1 o'clock afternoon of the day (Sunday excepted) following such presentation, or sooner if so ordered by the Senate, proceed to the consideration of such articles, and shall continue in session from day to day, (Sundays excepted) after the trial shall commence, (unless otherwise ordered by the Senate,) until final judgment shall be rendered, and so much longer as may, in its judgment, be needful. Before proceeding to the consideration of the articles of impeachment, the presiding officer shall administer the oath hereafter provided to the members of the Senate then present, and to the other members of the Senate as they shall appear, whose duty it shall be to take the same.
Once the motion is made in the Senate, the Chief Justice is automatically called upon and sworn in as the presiding officer of the impeachment trial. During the trial of Andrew Johnson articles were passed on February 29th in the House, introduced on March 4th in the Senate and the Chief Justice was sworn in March 5th. To give you an idea of the power wielded by the Chief Justice in such cases, Chief Justice Rehnquist was famously strict during President Clinton's impeachment trial, not even allowing Senators to leave the floor for the entire length of the trial once it began (to the frustration of many Senators).
As we speak there is no case that can be made against Trump that rises to the level of treason or high crimes and misdemeanors. If the Mueller investigation comes up with something bad then that's another story, but it's hard to believe at this point that such a transgression could have been kept a secret for so long. Which doesn't mean the Dems won't impeach Trump anyway, whether they actually have grounds to do so or not. One would hope that if they did so without just cause that they would pay a heavy price in the 2020 elections, same as the Repubs should if sufficient grounds did exist for removal from office but they wouldn't vote for that. Removing a President is serious shit though, it's never been done.