Go to the Projects page and click on the Project name. You can also click on "View Details" from the Actions drop-down menu (on the right).

Next, go to the Assignees section or click on "View All".

Turn on the Toggle for "Can Manage Project" for the specific member.

After you permit to Manage a Project to an employee, he/she will become the Project manager for that project and will be able to change the details of that project.

Once you grant a team member permission to manage a project, they become the project manager for that project and can edit its details.