This is a brief diary which is more of a pictorial explanation than anything else.
To me, not an engineer but with a science background, the top kill idea didn't make any sense, with that riser kinked and leaking where it comes out of the BOP. The idea initially shown below is that under very high pressure a dense and viscous substance ("mud") would be injected into the "kill" and "choke" ports, and that this pressurized substance would force the oil back down the well, and then would be cemented over. However, it seemed to me that firstly, the mud could not be injected very rapidly through the small hoses, and, secondly, the mud would just come flying out the top and rip the already leaking riser pipe into shreds.
Now I have run across an animation/explanation which makes the scheme seem more reasonable.