If you want to use the Dock without your mouse, press Ctlr+Fn+F3 on your keyboard. This will pop the Dock up (if it’s hidden) and will navigate to the leftmost item on the Dock. You can then use the right/left arrows on your keyboard to navigate between the Dock items.
To open one of the items in the Dock while the focus is on the item, press the Space or the Enter key.
To open the context menu for that item while the focus is on it, press the Up arrow on your keyboard.