Q:

How can I add new points to an existing path? 

I've drawn a path with the pen tool in Adobe Illustrator.  I did some other work, but now I want to extend the path with more points.  How can I continue drawing the path where if I click off of the path, it generates a new anchor point and connects it? 
I know I could keep adding more points along the existing path using the "add anchor point", but I'd like to keep drawing as if I had never stopped drawing the original path (click a new place on the screen, and the path continues to there). 

A:

With the Pen Tool start by clicking the anchor point at the end of the existing path.... then you can continue drawing. 
The pen tool icon will have a little / next to it indicate clicking will continue the existing path.  If you aren't exactly over the path endpoint, you'll see a * instead, which indicates a new path. 
 <-- Continue Path vs New Path --> 
 <--- if precise cursors are enabled

