Where are you based?
Find local bands/promoters/venues. Check them out first - are they the right kind of music/do they put on the right kind of music? Do they put on unsigned bands (no point approaching Coldplays booking agent for example).
This website is a good place to start:
http://getagig.info/Then approach them. Promoters/venues almost want to hear some music, so you'll need an mp3 or something.
Be honest. If they say you need x amount of fans to come, dont say sure whe you can't. It might get you somewhere to.
Be prepared to wait. Some of the more popular venues won't reply for a couple of weeks or more.
Enquire after your open mic's. Most places that do open mic's do full gigs too.
Open mic's are a gig in themselves anyway, so don't discount their power!
Me and my partner want to start playing open mic's in local pubs....I find it a particularly scary thing to do!
But I'd treat it like a proper (albeit short) sort of gig. Introduce yourself and chat like you normally would. Make it quietly know to the organiser that you will happily do more than the normal one or two perhaps?
If you do them regularly and are good, you never know, you might start pulling in a crowd to those open mic's and transform them into your own gig