Andy's given you sound advice.
For a start, see if you can find any casual work at local venues. That can be anything from catering and stewarding to rigging and helping with load-ins. You start at the bottom and gain kudos by how well you do your job, but there's something to be said for pushing yourself just a little too (not over the top, though - pros in that business can spot a pillock at 500 yards).
Another way is, again as Andy says, to get yourself on an Event Management course. My hubby's had several students on placement from the course run by De Montfort Uni here in Leicester, and he's generally impressed by the standard. One girl he had on placement went on to get some part-time work in the venue bar as well and has since gone on to work full-time for the council's Festivals Unit (partly due to the reference and experience she got from the placement). She's recently been responsible for programming a whole month's entertainment in Leicester's Town Hall Square. She still comes back to help out with the music festivals each year, gets to meet lots of bands and is making some useful contacts - bands, managers, agencies, promoters etc.