Only Admins can change a Project logo, and this feature is available to Admins of free Projects as well as Admins of Premium Projects.
To change the Project logo, go to the Admin tab within the Project:
The option to change the Project logo is here:
This will open a window prompting you to add a photo from your computer to use as the Project logo
Simply click on the image file you wish to use, and it will be uploaded as your Project logo:
Now that your logo has changed, be sure to click on "Save"