Identifying Shapes (basic)
There are several stages to identifying shapes (and classifications can often become more and more specific).
The first set of shapes that students typically learn are twodimensional or plane shapes (they have only two dimensions: length and width and occupy a plane).
Plane shapes are made up of lines and vertices (a vertex is a corner, where more than one line meet). Polygon is the general name for a "many sided" shape.
The first common shape is not a polygon, because it's made with just one line (and so no vertices), a circle:
The rest of the common shapes are identified first by number of sides and vertices and, in the case of squares v. rectangles, whether or not those sides are equal.
Triangle  Rectangles (not equal sides)/Squares (equal sides)  Pentagon  Hexagon  And so on.... 
3 sides/vertices  4 sides/vertices (quadrilaterals)  5 sides/vertices  6 sides/vertices  Septagon = 7 sides Octogon = 8 sides Nonagon = 9 sides Decagon = 10 sides 

See additional lessons for more shapes: Identifying Quadrilaterals, Identifying Triangles by Sides, Identifying Triangles by Angle, Identifying 3Dimensional Shapes.