OK... What you've written about traditional surrogacy is pretty accurate. The insemination can (but doesn't have to) be IUI.
Your description of the process of gestational surrogacy is a bit off. Though the cycles may be synchronized, the main point is that the woman who carries the baby is not its biological mother. The baby can either be from the intended mother's egg (the mother who will raise the baby) or from a donor egg. Likewise, the sperm can be from the intended father or from a donor.
If you want to know more about the actual process, it is the same as ivf, but the embryo(s) created are transferred to the surrogate mother.
Good luck with your essay!
Rachel Inbar
www.fertilitystories.com