Per the American Pregnancy Association:
Intrauterine insemination (IUI) is a procedure that involves placing sperm inside a woman’s uterus to facilitate fertilization. This fertility treatment does not involve the manipulation of a woman’s eggs, and therefore is not considered an assisted reproductive technology (ART) procedure.
Basically, sperm from the hubby is washed (to separate the sperm from the seminal fluid and to eliminate the bad or non-motile sperm from the good healthy ones), and placed in a medium in a vile. A catheter is placed in my uterus and the sperm are pushed in through a syringe. Hopefully egg(s) (in a normal woman, usually one egg a month is released. With fertility drugs we're hoping for 2 or 3) are released (you never really know through an IUI as on IUI day no ultrasound is performed (and eggs are to small to be seen anyway) and travel down the fallopian tubes where the sperm are anxiously awaiting.
Odds are not as good as doing IVF:
In Vitro Fertilization is commonly referred to as IVF. IVF is the process of fertilization by manually combining an egg and sperm in a laboratory dish. When the IVF procedure is successful, the process is combined with a procedure known as embryo transfer, which involves physically placing the embryo in the uterus.
Per Generations (Our RE (Reproductive Endrocrinologst)) Odds for an IUI are roughly 20%, IVF 50%. Though odds vary based up your personal factors and how aggressive the RE is.
Costs: Costs are much lower for an IUI (for us ~$3k a time (including drugs, the ultrasounds and the procedure)) vs. IVF (from $15-20k depending on your clinic).
We chose IUI as nothing is "medically" wrong with us. $3k a pop is much easier to swallow than $15-20k if it doesn't take. IVF is typically geared more for those with diagnosed problems or those wanting to be more aggressive. If we had all the money and time in the world we probably would have went with IVF, but we're realists here. Despite our best efforts, none of these procedures may work.
So there it is in a nutshell. Any questions?
Disclaimer: I am not a medical doctor, this is my knowledge from research, doctor visits and personal experiences.