Mrs Zero and I ran one while the normal host was on holiday, so I have a bit of experience.
People need to sign in when they get there. Some open mics have pre-booking, others are first come first served. The host does the first slot. At one that I'm house bassist for, which is pre-book, the host encourages collaborations so I have a vague idea of who might want my services and sometimes even find out what songs they'll be doing before the night (sometimes I find out shortly before going on stage, sometimes I find out when they start). Have an adequate supply of mics, mic stands, and guitar leads. If there's going to be a drumkit there, make sure there's also a drummer who can set it up there during setup time. Have a couple of music stands too.
If there's a Facebook page for the event, take some photos and stick them up after the event, maybe do a little acknowledgement of who was there - for example, https://www.facebook.com/profile.php?id=61578654727858 and https://www.facebook.com/groups/976913649517143
My personal opinion about running order: after a few times, you'll spot who arrives, plays, and then f*cks off without staying to watch anyone else. Put them on late. Generally rotate order for the regulars so none of them get permanently stuck with early or graveyard slots and put irregulars into the better but not prime slots.