What is the Parallel Axis Theorem?
The parallel axis theorem can be used to determine the moment of inertia of a rigid body around any axis. Oftentimes the moment of intertia of a rigid body is not taken around the centroid, rather some arbitrary point. A good example of this is an IBeam. You may need to use the parallel axis theorem to determine the Moment of Inertia of an IBeam around it's centroid because the top and bottom flange will not be acting through the centroid of the shape (see the Example Below).
Using the Parallel Axis Theorem  
How can I calculate a moment of inertia using the Parallel Axis Theorem
Figure 1: Variables used for using the Parallel Axis Theorem
Once the centroid of the shape is found, the parallel axis theorem can be used around any axis by taking: I_{A} =\sum ( I_{x} + Ad^2)

where:
 I_{A} = The moment of inertia taken about the AA axis (in^{4})
 I_{x} = The moment of inertia taken through the centroid, the xx axis (in^{4})
 A = The area of the rigid body (in^{2})
 d = the perpendicular distance between the AA axis and the xx axis (in)
Note: Looking closely at the Parallel Axis Theorem you can see that the moment of inertia of a shape will increase rapidly the further the Centroid of the area is from the axis being checked.
Using the Parallel Axis Theorem in an Example
Figure 2: Parallel Axis Theorem Example
For the above example, take h = 12", h_{1} = 10", b = 9 " and t_{w} = 1". Solve for I_{x} using the Parallel Axis Theorem.
1) Solve for I_{x} of the center section (feel free to use the shortcuts here?:
{ I_x}_{web} = \frac{bh^3}{12} = \frac{1" * 10"^3}{12} = 83 in^4
{I_x}_{flange} = \frac{bh^3}{12} = \frac{9" * 1"^3}{12} = 0.75 in^4
2) Solve the increase in the moment of inertia for A_{1} using the parallel axis theorem:
A_1 = 1in * 9" = 9 in^2
d = \frac{12in  10in}{2*2} + \frac{10in}{2} = 0.5in + 5in = 5.5 in
Ad^2 = (9 in^2)(5.5in)^2 = 272 in^4
3) Using the Parallel Axis Theorem:
As you can see a majority of the Section Modulus (87%) comes from the parallel axis theorem and not from the moment of inertia calculation.
Resources:
 Paul A. Tipler, "Physics for Scientists and Engineers (4th Edition)", 1990