Who presides over the US Senate on a day-to-day basis?

Question

In the Senate, they always seem to be addressing "Mister President" or "Madame President", and occasionally the presiding Senator says something - but it's never clear who that is (I listen to political news and speeches on the radio rather than TV, so I don't get to see the faces).

I don't think it's Orrin Hatch (Pro Tempore), at least not often - and it's rarely or never Mike Pence (VP/President of the Senate).

So I'm assuming Hatch or McConnell (Majority Leader) just picks someone to sit in the chair - do they rotate? Or is it whoever they feel like picking that day? Or do they draw straws?

Answer 1

The duty of presiding over the Senate is usually given to Junior senators in rotation to help them learn how the Senate works.

For example Hillary Clinton was first given the task of presiding in January 2001, shortly after she was elected to the Senate.

CNN noted at the time:

It is customary for new senators to preside over the Senate to help them learn parliamentary procedure.

...

Although Republicans hold the majority [...] under their power-sharing agreement, Democrats are allotted time to preside over the chamber for a limited amount of time each week.