How do you actually start a meeting? The guidance refers to screens I just don't have.

Welcome to the Zoom Community, @Stupidsystem.

What screens do you have? A lot depends on whether you’re looking at the Zoom Web Portal, or the Zoom Client App; and if you’re looking at the Client App, which device and operating system are you using?

This Zoom Support article has information for each system:

https://support.zoom.us/hc/en-us/articles/201362423-Starting-or-joining-a-meeting-as-the-host

Let me know if you still need help after referring to that document. 

Sign in to your Zoom web portal. Click Meetings. Under Upcoming, click Start next to the meeting you want to start. The Zoom client should launch automatically to start the meeting.