In order to download a shared server project, navigate to the Shared With Me projects page and select the target project. Toggle that project's dropdown and select Download. This will bring up the Download Project popup.
Alternatively clicking on the Download icon on the project or in the projects details page will bring up the Download Project popup.
After clicking download you will encounter the download popup asking how you would like to download the project. Based on your level of permissions you will be presented with 2 of the following 3 options:
Linked: This will download a local copy that is connected to the online version. Any changes you make to your local copy can by synced to the online copy if you have the edit permission.
View: Download a local copy of the project that is linked to the online version and can download new changes made to the online version only. In this case, you have read only permissions so you will be unable to sync any changes you make to this lesson.
Separate: This will download a completely separate local copy of the project unconnected from the online version so that you can freely make changes and upload it as your own project.
Once your project is downloaded you can begin to edit the lessons within it by click on the "..." menu in the top right corner of the lesson entry and press "Edit" or create a new lesson within the project by pressing the xplorer logo with a plus at the top of the project detail page. Both illustrated in the image below.