How do I record a Microsoft Teams meeting, and where does the recording end up?

In the meeting, click More options (…) in the toolbar > Record and transcribe > Start recording. You don't have to be the organizer, but you do need to be in the same organization with the right permissions (external guests usually can't). Everyone is notified when recording starts. When it ends, the recording saves automatically to OneDrive (SharePoint for a channel meeting) and a link drops into the meeting chat for people to watch.

The auto-save to OneDrive plus a link in the chat is the handy part, no hunting for the file. Anyone in the meeting finds it in the chat afterward.

Permissions are the gotcha. If Record is missing for you, your admin has restricted it or you're an external guest. An internal member or the organizer has to do it.