I'll give you a true example. I do standup comedy. I started going to a comedy night on a regular basis as a punter and talking to the compere and organiser. After a while they wanted someone to help put the chairs out and this got me in for free. I then ended up doing the sound and I still do on occasion. It was this chain of events that then allowed me to ask the compere, (he comperes for quite a few venues), to get me an open spot somewhere. I got as much stage time as possible at other venues through comedians I met and this is how I think it is a good way to start. Don't expect to be paid or only very little pay initially and get as much stage time as possible.
Which area of the country are you in, many councils do arts listings in magazines/websites etc or there may be a venue in a nearby town that does this sort of thing already. Contact any performing arts groups in the area and see if they can give you a contact number of someone who can help. It's like any other industry, it's not what you know but the people you know that counts. That old unassuming bloke sitting quietly in the corner of a theatre may actually be a film/theatre producer or agent.
Also try theatres, the stage manager usually knows most people locally who run the sort of events that you need. Phone and get a name and if possible arrange to meet them. A meeting shows more commitment than just phoning around. Be yourself and above all be professional but not a Prima Donna. It's a difficult area to get into, I would also suggest doing a short piece of your own work, 5 mins tops, to show that you can work on your own initiative. I know there's alot of points mentioned her but good luck and keep trying.