Answer:
It varies by type of IUD, and if you have insurance, what type and if it's covered by that. I have Blue Cross Blue Shield, and it is covered through that, but I'd call yours to make sure. The true cost of my Mirena IUD was around $1100, but the cost to me was about $25. That's because 1) it was covered in my insurance, and 2) my doctor did it during a regular check-up visit.
Another thing to consider is the cost of an IUD versus the cost of the Pill over the course of the 5 or 10 years you have it. I was paying around $25/mon for the Pill, which works out to 300/yr or 1500 over 5 years. So even if I didn't have insurance, the cost of the Mirena would still have been less than the cost of my Pill. Also, IUDs are generally more effective than the Pill because they're considered "idiot proof" - you can't "forget" to take something that's inside you. That was really important to me, but you could be much better than I was at remembering your Pill.