I had my first (and hopefully last) kidney stone a couple of months ago.
It started out with a general upset stomach sort of thing - felt like I might have diarrhea.
I took Pepto Bismol (bad idea) and threw up a couple of times (so hard that I burst several small blood vessels around my eyes - it looked like I had red freckles).
The pain increased but was concentrated on my left side, just below my ribcage, both front and back. I couldn't be still - I couldn't stand, sit, lie down, lean over, kneel, crouch, lay on my back with my feet up on the wall - believe me, I tried every position I could think of. The pain became excruciating and I finally went to the emergency room (where I sat for several hours).
They did a CT scan and it showed the kidney stone. By the time I met with a doctor, the pain had receded quite a bit. They gave me a prescription for Vicodin, instructions to make an appointment with a urologist, and a stupid little plastic funnel with a screen so I could strain my urine and catch the little bugger if I passed it on my own.
I ended up having minor surgery to remove it two days later.
The urologist told me that I would feel the worst pain when the stone was leaving the kidney and entering the ureter, then when it passed over a bundle of blood vessels near my pelvic bone, again when it entered my bladder, and again when it exited my bladder and made its bid for freedom.
So that was the long answer to your question. The short answer is PAIN. Lots and lots of pain concentrated on one side or the other, often in your back. Excruciating pain that literally makes you beg for your mommy.