Bring up the Pen tool using the icon on the left-hand toolbar, or use the shortcut P. The Pen tool on Affinity Designer is incredibly similar to other Pen tools you have used elsewhere.
Affinity's Pen tool has four different modes. First, there's the basic Pen mode. Smart mode will assist you in creating flowing curves that naturally arc.
You've created a path using your Pen tool, you can adjust it using it using the conversion tools shown in the image above.
There are also a number of actions to choose from.
Snapping is used in a variety of ways in Affinity Designer. For the Pen tool I recommend you play about with the different settings to figure out your preference.