Hoe do I correctly determin the square footage of a property?

Find a book on surveying. You can find it online as well.

Multiply the length by the width. There are also handy calculators all over the web.

Here is one I use
Square Footage Calculator (http://www.bhg.com/bhg/story.jhtml?storyid=/templatedata/bhg/story/data/16144.xml&catref=SC1960)

If the property is a strange shape (i.e. not a rectangle or a right triangle) divide it into pieces which are rectangles and/or right triangles. You probably know the formula for area of rectangle is width*height and right triangle is 0.5*width*height. Then sum up the area of all these pieces and you're done.

I surveyed for years and have calculated many area of plots. Do you have any info you can post(bearings, coordinates of corners, etc.). I will attempt to calculate it for you.