Basic Fin Shapes:

Image Source: Leisure Pro

Basic Types:

A: Heterocercal
       Vertebrae extend into upper lobe.
B: Protocercal
        Vertebrae extend to the tip, and the tip is tapered.
C: Homocercal
        Vertebrae extend into upper lobe, but only a
            little.
D: Diphycercal
        Vertebrae extend to the tip, and the tip is dorso-ventrally expanded a little.

Image Source: Fishionary