As companies reach beyond their boundaries to find and develop ideas, they are exploring new models to manage innovation. In projects that tap external talent, questions quickly arise about process management, intellectual-property rights, and the right to make decisions. Some executives have been at this game longer than others. Mitchell Baker, chairman and former chief executive officer of Mozilla Corporation, has devoted the past ten years to leading an effort that relies extensively on people outside her company—not just for creative ideas, but also to develop products and make decisions. The result: Mozilla’s Firefox browser, with 150 million users, has become a rival of Microsoft’s market-leading Internet Explorer.

As Firefox flourished, the process that created it became a model for participatory, open-source collaboration. Baker’s role, central from the beginning, has taken many twists and turns. Ten years ago, she was a software lawyer at Netscape Communications—which developed the original commercial Web browser—when the company decided to release its product code to the public. Baker’s interest in defining and managing the project quickly earned her a place as one of its leaders. She continued to guide the project after Netscape was acquired by AOL, led the subsequent spin-off (to the nonprofit...