As a meeting host, you need to manage the participants, to a limited degree. It's a bit like managing a physical classroom full of your students. (Although in a physical classroom there is no clickable button to instantly mute one or more participants!)

Where to Find Your Participants

Once the Zoom window opens and you are viewing the live webcam feed, there is a black bar along the bottom of that window containing various features to use, including "Manage Participants".

Toolbar at bottom of Zoom video window

Click "Manage Participants". The Participants pane should open on the side of the Zoom window. At the top of the pane, you should see your name as the Host of the meeting.
Beneath your name should be a list of the names of the participants.

What You Can Do with the Participants Pane:

There are tools at the right side and bottom edges of the pane you can use to manage whether the participants are muted or microphone-enabled.
There are also small emoji-like icons you can click to display next to your own name, to express yourself. The participants have the same icons they can use as well.
You can pop out the pane as a separate window:
1. Click the tiny down-pointing chevron arrow in the upper left corner of the pane.
2. Select "Pop Out".
3. You can click-and-drag to resize and/or move the pane independently of the video window.
4. To return the participants pane back to where it was, click on the "More" button in the lower-right corner of the Participants Window, and select "Merge to Meeting Window".

Merge Participant Panel into main frame screen shot

To prevent participants from screen sharing:

In the host controls, click the arrow next to Share Screen and click Advanced Sharing Options.
Under Who can share? choose Only Host.
Close the window.

Support

Need support for managing your participants and your meeting?

There are many options for managing participants in a Zoom meeting, which can be quite a responsibility in addition to teaching! Many instructors opt to assign an Alternate Host or have a Co-Host as a "second set of hands" to help manage participants and chat questions. Each option has different capabilities and set up instructions.

During the Meeting: Select a Co-Host

To select a Co-Host, simply hover over the participant and click "More". A pop-up window will appear. Scroll down and select "Make Co-Host"

To see other participant options, hover over an individual participant, and click the "More" button:

To find out more about the kinds of things a Co-Host can do, click "What can a Co-Host do?"

Before the Meeting: Assign an Alternative Host

The alternative host option allows you to schedule meetings and designate another Licensed user on the same account to start the meeting or webinar if you are unable to. This user will receive an email notifying them that they've been added as an alternative host, with a link to start the meeting. The alternative host will need to use the link in the email or have the calendar invite sent to them by the original host and use the join link there.

You can also give another Licensed user scheduling privileges, which will make them an alternative host for all of your meetings and webinars and allow them to schedule meetings for you. If both users have a webinar license, they can also schedule webinars for you.

Additional Tutorials

To find out more about what options you can set from the Participants Panel, click "What You Can Do with individual participants in the Participants Pane"

To find out more about what Alternative Hosts can do, click "Assign an Alternative Host"

To compare Host vs Alternate Host vs Co-Host, click "Meeting Roles: Host vs Alternate Host vs Co-Host"