The two options available are "live" transcription (captioning typed by a person attending the meeting) and post-meeting captioning through a service.
Events, not a part of core instruction, will need to provide a recharge number or pay a 3rd Party directly for coordination of these services.
For Instructional Support, Captioning of Zoom meetings is an add-on feature that is currently only available in conjunction with the Disabled Students Program (DSP). See this article if your meeting is for a registered course and you have the support of DSP: https://help.lsit.ucsb.edu/hc/en-us/articles/360042185611-Zoom-Transcription-and-Closed-Captioning-of-Zoom-Sessions-for-classroom-instruction
"Live" Professional Transcription Method:
UCSB has been using the services of LNS to provide live transcription captioning. You may contact them directly to support your meeting/event or contact Instructional Development (firstname.lastname@example.org) to coordinate it for you for an admin fee of $75.
LNS will provide a transcriptionist to join your live Zoom session and you will be provided with instructions to setup your meeting to allow for this.
The live captioning runs around $175 per hour, with a setup time of about 15-30 minutes before the start.
The Host records the session, they upload to GauchoCast, and the videos are sent out to Verbit for captioning of the recording. If the Host does not have access to Gauchocast it may be possible to provide ID the video file via Box or Google Drive.
Verbit charges approx $.84 per minute for this service. ID will need a valid Recharge number before ordering.
Arrangements for Verbit captioning can be had by email to email@example.com
"Roll your own" Live Captioning
It is possible to create live captions from within a Zoom session and record them for free.
Someone in the meeting can be designated as the captioner and their keystrokes will be visible and can be captured "live". It would be wise to practice this method to determine if it is adequate for your needs.