You can create shapes using the Pen Tool, or you can use the shape tool to drag out an image on the canvas. Once you've drawn a shape, use the Edit Object button in the toolbar to quickly enter vector edit mode.
When you're editing an object, you can interact with the existing points and the lines between them. You can also use the Pen Tool to plot additional points and manipulate those as well.
Paths between the points can be straight lines, or you can curve them using the Bend Tool to activate Beziers.
Use the Command + Click shortcut on any point to turn on the handle controls.
If you haven't already, check out The Bezier Game and learn how to master the Pen Tool.