First you have to remember that it feels and looks a LOT different to us looking out the front window as opposed to those tiny things you have to look through.
And I can virtually guarantee that it isn't as bad as it feels.
Turbulence is graded from Light to Moderate to Severe. I have only once encountered Severe turbulence in nearly 10 years of flying.
I can't recall the exact definitions but -
Light turbulence is just your bog standard day really
Moderate is when the aeroplane starts to move around a bit more and walking and moving become a bit of an effort.
Severe is effectively when the aeroplane is, not out of control per se, rather difficult to maintain the required attitude and level. But as far as controlling the aeroplane there are no real problems.
I would say it's almost impossible to predict accurately when and where turbulence will occur and what magnitude it's going to be. You have a general idea from wind strength and direction that sort of thing but sometimes it just happens out of the blue!
If by capabilities you mean aircraft 'G' limits then most if not all airliners are stressed to +2 1/2 g and - 1g and I think you'd have to be trying very hard to exceed these.
My worst experience was in a BAe 146 over Villatobas VOR in Spain.
We were climbing to FL 280 and popped out of a layer of cloud just before we levelled. Looking about half a mile ahead we could see what is called a "Rotor", imagine a horizontal whirlpool of cloud, right in front of us. It was to late to do much about it, switch the seatbelt sign on, PA to the cabin crew to sit down, quickly! And slow to our rough airspeed.
We hit this thing, the autopilot disconnected (maybe should have been out all ready) and ended up going through about 45 degrees of bank to the right at the same time as losing about 400ft and about 50 knots. And then it was back the other way...About 40 degrees roll to the left and up about 800 feet. Skipper trying to maintain speed and attitude. Me a VERY laconic call to ATC. "*****123 unable to maintain altitude due severe turbulence" "Roger" in a Spanish accent...I remember it clearly to this day!
About 10 seconds later we'd come out the other side and it was smooth as a babies bum. Quick check with the cabin to see if everything was ok, it was
Please remember though that aircraft are designed and built well and don't just fall out of the sky willy nilly...although it may feel like it.
I get a little bit anxious as a passenger in turbulence. I think this is because it's almost impossible to see a decent horizon from the cabin and therefore get your bearings. The best thing to do is probably look out the window anyway!
Hope my rambling is of some use and I hope that somebody with more technical knowledge will be able to clear up some of my nebulous words