The Gnome wiki does a very good job of explaining this so start there and read on for quick tips.
Super ALT S now enables or disables Orca screen reader.
Super M move to the message tray, for missed notifications or chat messages.
Super A Move to the activities view
Record your Desktop right from Gnome-shell
Shift ALT Control R
You may be used to using keyboard shortcuts in a specific way, this will try to show you the differences for Gnome-shell.
In Unity to access the menus or indicators we use
In Gnome-shell we use
If you don't like or have trouble holding
Shift Control Alt arrow
To move an active application to another workspace, you can do it in Gnome-shell by
Choose from the workspace menu items to move to a specific workspace or up/down.
When launching applications from the dash
If you want to open another instance of an application, such as Nautilus, when you type the name and hear Orca speak it, pushitem
You can also right click for extra options with