#1 Use the line tool and then fill it in with the bucket tool
This is one of the easiest way to create large polygon tool, draw a series of line segments and make sure you connect the ends. You can then use the shift key to quickly drag the view to complete the polygon.
When you hover over the end of a line you can quickly continue it. You will see a dark black circle around the end indicating you will continue the line.
Once you have the boundary drawn, you can use the bucket tool to fill it and create a polygon
#2 Use a rough polygon and add points
The second method involves creating a large rough polygon and then zooming in to make it more detail by adding midpoints. As an example we created a rough polygon for the boundary for New York as seen here.
Using the edit tool, you can then zoom in and make the polygon more detailed by adding and dragging mid-points like below.