New Path: Your next click will begin a new path.
New Point: Your next click will add a segment and a point to an existing path.
Close Path: Your cursor will look like this when you hover over the beginning point of the active path. Your next click will close the path.
Add Point: When you hover anywhere on a segment of a selected path your cursor will change to this. Your next click will add a new point to that path segment.
Delete Point: When you hover over an existing point on a selected path, your cursor will change to this. Your next click will delete that point.
Modify End Point: When you hover over the active end point of a selected, your cursor will change to this. Your next click (and hold) will allow you to modify the anchor point handles.
Add To Open Path: When you hover over either end of an unselected path, your curosr will change to this. Your next click will select the path. Your second click will add a segment to the path from the selected anchor point.
Convert Point Tool: You will use this tool to adjust the handles on an existing point. Hold your cursor over the point that you want to adjust and hold down the <option> key.
Direct Selection Tool: Access this tool by holding down the <cmd> key while you have the pen tool selected. Use this tool to select a path that has been deselected. Also use it to select individual anchor points on a selected path - then move the selected point or move the anchor point handles.