Using paths

Adobe Illustrator gives you several tools to use to draw paths.  The tools are located in the tools window on the left side of the screen.  The tool options for drawing paths are the pen, pencil, paintbrush, rectangle, rounded rectangle, ellipse, polygon, star, and spiral. 
Once you have selected your tool, you may draw a path on the document.  The shape tools draw paths with either straight or curved sides, depending on the shape.  The pen may be used to draw a straight or a curved path while the pencil and paintbrush draw only curved. 

Adding/Deleting points on a path
You may use the Add Anchor Point Tool or the Delete Anchor Point Tool to add or delete a point from a path.  These tools are hidden under the pen tool in the original tool box. 

Editing paths
You may use the Direct Selection Tool to change a path that is already drawn.  Simply click on a point already on the path and move it, or click on a line segment of the path to move it.  You may also change the type of specific points.  To do this, select the white Convert Anchor Point Tool from the tools window.  This tool is hidden under the pen tool in the original tool window.  Click on the point on the path you wish to change.  The Convert Anchor Point Tool changes curved points to corner points with one click, and corner points to curved points with a click and drag.  The shape of a path can be changed by editing its anchor points.  You can control curves by dragging the direction points at the end of the direction lines that appear at anchor points. 

Adding text to paths
From the tools window, select one of the path type tools (hidden under the type tool in the original tool window).  Click on the path you wish to add text to and a blinking cursor will appear on the path.  You may then begin typing.