Actually, I think, if I understand it correctly, you avoid fat the day of (and even the day before if you want) of the flush to build up the bile. Bile is released when fat is introduced to your system, so not taking in fats for 12/24/36 hours before downing the olive oil allows for a buildup of bile. Dumping so much olive oil all at once signals the body to let loose the built up bile helping to 'push' the 'stones' out.
The reason many flushes include Epsom Salts is they dilate the bile ducts allowing for the stones to pass through. As Valerie said, apple juice/apples/malic acid is recommended to soften the stones making them pass through the bile ducts more easily. I'm still trying to get a handle on the grapefruit/lemon juice part, but it seems it "speeds the transit of the olive oil thru the stomach and into the duodenum, which helps prevent or minimize nausea." (That's from W.D. Kelley's Liver Flush found HERE.)
So far, I've not suffered from nausea and I tend to sleep Better during a flush. I do get an increase in this weird rolling/pinching feeling right below my lower/floating ribs towards the center of my abdomen that may coincide with releasing larger stones, but it's not painful, more just a little uncomfortable. During a flush it seems to last until the diarrhea finishes (about 20 hours after the OO.GF for me.) I don't notice it again until after a week or two - I did have this feeling for a few months, since back surgery, off and on whenever I ate, so having it fade is a rather nice benefit.
Oh, and not many mention the smell, but I've noticed one and it is different than 'normal' bowel movements - possibly the bile. It passes soon, too. Be warned, many people experience a burning sensation when passing the stones/bile. I did the first 2 flushes, but not this time. Andreas Moritz has addressed this on his forum here and I believe his view is that crystals from the gallbladder may be passing through and irritating.
Keep reading and start flushing! Your body will ultimately love you for it. =)