Once you succesfully connect Origami to Adobe Illustator, you should see a 3D scene with your shape there. If you haven’t yet created a die-line in Illustrator, you will see just a 3D grid.
The Origami window has a toolbar at the top where you can reload the scene, fit the shape to the window or save the current scene as an image or as a 3D model.
See here for more details on working with Illustrator.
Use the Paper menu to set up paper thickness. You can choose a specific thickness, or select No thickness to make the paper completely flat.
Use the View menu to configure background colors, field of view settings and some other options like floor grid and debug information.
You can rotate the camera by holding down the left mouse button and dragging the mouse. You can also pan the camera by holding down the right button. A nice way to reset the camera is to use the “Fit to view” option that sets the camera to the best position for the window’s proportions.