I need to write up how to find a greatest common factor in a polynomial. I am having a hard time doing so. Could someone help me please?

Do you mean greatest common factor in two polynomials?

I would factor each one, circle the common factors, and multiply them together.

For example:
x^3-1 = (x-1)(x^2+x+1)
x^2-1 = (x-1)(x+1)

The only common factor is (x-1), so the GCF is (x-1).