Here are tools, windows, and menu items that you should acquaint yourself with in Project 1:
Selection Tool
Direct Selection Tool
Pen Tool (create and edit Anchor Points/Bezier curves)
Here are a few tutorials for drawing with Shape and Pen tools
2 video tutorial of Line, Shape and Eraser tools
Rectangle (Ellipse, etc.) Tools
Rotate
Scale
Free Transform
Menu Items:
Object
Transform: Move, Rotate, Reflect, Scale
Arrange
Group/Ungroup
Lock
Window (Dialog Boxes)
Align
Color
Layers
Pathfinder
Stroke/fill