You already use logic models If you use "if, then" reasoning, then you're using a logic model. Writing down a logic model facilitates understanding and communication.
A simple tutorial with audio is available here. We particularly recommend the "If Then" section, #11. We think it belongs at the beginning, but since this was written by another organization, that's not our call.
The non-profit group Innovation Network provides an online logic model tool. This is comprehensive, at the expense of requiring more time to complete. Registration is required.
Wikipedia - Logic Model article, with references to applications in - organizational assessment (e.g., Malcolm Baldridge Award) - strategic planning - program planing and evaluation - performance measurements (e.g., balanced scorecards, KPIs) - process improvement (e.g., TQM, Six Sigma)