The best place to start is looking at it from their perspective - what will they gain by being involved in the school? For elected officials, especially the ones that represent the district the school is in, they will want to closely associate their work with the success of the school - what initiatives are they backing or pushing? Read some minutes from the most recent minutes and use the officials own words to connect what they are passionate about with your school. Same things with board members and community organizers - I think as the coordinators, it is our job to interpret why our work is so important to others.
For businesses, there is the big picture of creating a more educated workforce locally for them. Ask them what they are looking for in the community? Find what drives them and then, again, connect those passions with the day-to-day activity and big picture goals of your school.
I've been most effective with elected officials, school board members, and community organizers. I find out what they're interested in and integrate that into my monthly "collaborative" meeting, giving them time to speak, making sure what they share ends with engaging the others in the meeting, etc. Businesses have been harder but some will come occasionally. It's all about finding out what they're most interested in and then catering at least a piece of the meeting to that. I also make sure my meetings are most about people working together on an issue or topic and LESS about people just sharing information out. People need to be working together, not passive.