As a session host ...
It's important during the marketplace and the event to know who added a session to the agenda. You can optionally link your name to your website, Twitter-, LinkedIn- or any other profile, so that people know who is the session host.
This helps participants and later visitors of the event's website to get an idea and starting points what your session was about. And of course it supports the knowledge sharing that's happening in your session. It's easiest capture the results directly on the card in the session agenda board. However, feel free to link to any other resource, such as a Google doc, Jamboard, a Mural or Miro board or any other tool that works for you. This capturing is sometimes also called "harvesting".
Depending on the reasons why you proposed a session, your session's conversation might need some guidance and/or facilitation in order for not being dominated by a few. You as a session host should provide this guidance.
However, depending on your session's participants, very little guidance might be needed, and it's also more than ok to ask for help in facilitation, during the marketplace or during your session.
Capturing the session results and topics might be helpful when facilitating as they can serve as a reminder what was talked about already and what you still might want to share. However ...
People might drop in and out of your session. That's to be expected and even encouraged at an Open Space. The Law of Mobility (sometimes also called the Law of Two Feet) tells every participant to decide for themselves if they feel they're contributing or getting something out of a session, and to go somewhere else if that's not the case.
In the beginning this might feel uncomfortable, seeing people leave and others joining. And you might wonder how to integrate late-comers to into your session.
In this case the Whatever happens is the only thing that could have and the Whoever comes are the right people principles can be helpful.
Be prepared to be surprised and see where the session goes. You decide for yourself what to make of the session, if you want to bring late-comers up to speed with what happened already or if you let them just lurk.
Besides the principles and one law (and the #humansconf Code of Conduct) there are no rules as to what should happen at an Open Space, and you're free to use the time and space however you wish.