Project is basically a folder with project configuration (including template variables and environments) (.puppetryrc), git configuration (.puppetrygit), reusable snippets file (.snippets.json) and suite files (*.json) . Project also keeps information about all latelly opened panels, expandable rows.
You can use hotkey Ctrl+S (⌘S) to save project (and open suite).

Create New Project

To create a new project you can press Ctrl+Shift-N (⌘⇧N) or click on File / New Project item in the main menu:
New Project in the main menu
It will open the following modal window:
New Project modal window
You need to provide project and suite names in the corresponding fields and use Browse... button to select project location. Then you press Create button.

Open Project

To open project you can press Ctrl+Shift-O (⌘⇧O) or click on File / Open Project item in the main menu:
Open Project in the main menu
It will open the following modal window:
You need to use Browse... button to select project location. Then you press Open button.

Edit Project

When you have a project open, you can still change the project name. Click on the edit icon next to the project name in the application header:
Edit project icon
It opens the following modal window:
Edit Project modal window
So you can provide a new name and press Save button.
This modal also has a read-only field App data directory, showing where the Electron project is located (application storage, run-time tests export and so on)

Save Project As..

You can clone the project to a new location. To do it click on File / Save Project As... item in the main menu:
Save Project As.. in the main menu
And select a new location in the following modal window:
Save Project As... modal window

Project Page

If you close all the application tabs you can see the project page:
Project page
If you forgot the physical location of your Puppetry project, use Project page to find it out

Project Explorer

You can find the project explorer window below the main menu as soon as you have opened the very first project. The explorer helps you to switch between recently opened projects and manage the list of active project suites.
Project explorer
Right in the header there two buttons. The first one to create a new project.
Create new project
The second button is to open an existing project.
Open project
In order to focus a project or suite you click on it once. To open a project or a suite you double-click on it.‌
Right-click on a suite opens the context menu where you can choose an action: open or delete (suite file):
Suite context menu‌
Right click on project displays the context menu where you choose between open project and remove project from the list. The last one doesn't physically remove project folder, but simply won't show it anymore in project explorer unless you open via main menu again.
Project context menu