I had the Essure procedure a bit over a year ago.
It went very well - really it was just like the website described. I was still breastfeeding my dd at the time, and having the essure done didn't interfere with that at all, since it's an outpatient procedure with minimum medication necessary (I took high doses of advil and one stronger pain pill right before the procedure, advil for a few days after the procedure. The gyn who did it usually also gives an anti-anxiety pill, but I chose to go without it and was fine.)
The most stressful part was worrying that I would get pregnant during the three month waiting period. But we managed, and the HSG test to confirm the tubal occlusion was quick and easy.
The worst part of the procedure was getting the local anesthetic shots in my cervix. Also, you do have to have a speculum in for a significant period of time - maybe ten minutes. I hate speculums and this was perhaps the worst part for me. Fortunately, the speculum can come out once they get the camera in. After that point, the procedure was easy and perfectly comfortable. I got to see the inside of my uterus on video, which was actually really cool. There was a slight twinge with the placement of each coil, but it wasn't a big deal. The whole procedure was quick - maybe 30 minutes. Shortly after it was over, I felt pretty normal again, just crampy like with an especially bad period. In fact, I actually ended up going shopping and out to dinner right afterward.
After a couple days, the cramping had stopped. Over the next few months, I occasionally felt a little twinge in the area where the coils were, but nothing else. My periods seemed a little heaver than usual for a few months, but that could have been because dd was nursing less.
Now, over a year later, I feel totally normal. I don't think the essure has had any side effects for me - and it's great that I don't have to worry about birth control anymore. The only real downside was the expense - thousands of dollars.