Before you learn how to work with objects on layers, you will need to get a basic understanding of the various operations you can perform on your layers.
There aren't any keyboard shortcuts dealing with layers. Everything you need to do with your layers is found in the Edit | Layers menu. You will also find the most used commands using the Action button ( ) found in the bottom of the Canvases Sidebar.
If you right-click on a layer in the sidebar, you will get access to the same layer menu commands as are found using the Action button.
You can add a new layer by either using the Edit | Layers | New Layer menu ...