I've played at dozens of open mics, in Florida and in Maryland. Only once have I seen someone just jump up and join in w/o asking and the host put a stop to it very quickly.
I've seen lots of different open mics formats. One of the more interesting is you put your name on a slip of paper and that is placed in a fish bowl. The host starts by drawing a name. That person gets ready, while the host plays two songs. Player one goes up to the mic, draws a name and announces that before playing. So on and so on.
On the host side he/she needs to manage the stage, control the sound and keep things moving. Don't let things drag between sets. Players need to be ready to go. Tune up before you hit the stage, decide what you are going to play, quick sound check and go. Don't go up, take your guitar out of the case, tune up, yell "hows everybody doin" in you best rock and roll voice, fiddle around some more, adjust the e.q., then mull over what you are going to play.