I would like to make one of those 600fps slow motion clips that can are on YouTube. such as this. I know it can be done in AE but I cannot figure it out.
As 50ndr33 says, you need to shoot/capture at as high an FPS as possible. The more FPS the better the slow motion effect afterwards.
Kronos is also a great plugin, but as he also states - it has some problems when footage isn't linear. If that's the case, you should have look at Twixtor. It's a bit more advanced (and more expensive) but it's better at handling advanced remaps, and gives you pin-point control.
This footage was probably around 24 fps.. If you want to slow it down to 50 % of the speed you would need to shoot at 48 fps to be able to get 24 fps when played back in 50 % speed. If you don't you can see that it is a series of pictures animated. And if you shoot at 24 fps and slow it down 12 times you get only 2 pictures per second.
BUT, there is fortunately a great way of making the computer generate the frames in between the frames that are actually there! So you could make it generate 9 pictures between each real frame thus resulting in a source clip with a fps of about 240! If you capture at 60 fps, which is possible you can get 600 fps. And the magic software that does this is called:
I've used it and it works great! It works, as far as I have noticed, by making a vector of the two images and animating that vector in between the two images that it is filling in frames inbetween. All natural movements are slowed down perfectly, but for example explosions can look a bit fake becaue they don't have a linear movement, not in terms of speed or in terms of position..
I hope this software will help you on your way!