For example, if my coworker and me are sitting at the registration desk, are we both able to use our log ins and register attendees?
Sure, as long as you both have access to the event.
Awesome - do they need to have separate Marketo log ins? How do I ensure they have access to the event?
Yes, you will need separate logins. More information can be found here - where you do need to give each person access to do this:
Event Check-in - Marketo Docs - Product Docs
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