Remove the T6 torx screw and the T10 torx pivot screw. Take a thin blade (putty knife etc) and gently pry the two halves of the knife handle apart. The pivot will likely make this a little difficult so keep the sides parallel and work at it gently.
The result will give you this (taken before cleaning):

A couple of things to note:
There are two copper/bronze washers - one on each side of the blade. One is larger than the other. Keep track of which side they are on. Because of the dirt it's pretty easy to see where the small one goes (in the above photo) - it goes on the torsion spring side. There is a steel pin between the liners just back and above the blade pivot. It is removable so don't loose it.
The torsion spring is the piece of wire between the steel liner and handle on the side opposite the clip. It can be seen in the photo.
The stainless liners are held to the inside of the handle halves by two small philips head screws. Feel free to remove the liners and observe the position of the torsion bar before lifting it out. It isn't under pressure so shouldn't take off on you.

Clean up the liners, the handles and other parts and put a bit of thick grease in the area of the handle where the torsion bar sits (you will likely see some grease there when you take it apart). I rubbed some grease on the bar itself.
Install the liners with the small philips head screws (2 per liner), positioning the torsion bar under the applicable liner. Take the opportunity to lightly oil all parts before putting them back together.
I assembled the unit starting from the clip side of the handle.
Ensure that the pivot is in place in the handle. Place the stainless pin in the hole in clip side liner. Position the blade with it's two copper washers on the pivot and gently press it down. Install the opposite handle and gently press the assembly together. Swing the blade almost closed and make sure that the blade end of the torsion bar fits into the hole in the blade. The other end of the torsion bar fits in the small slot in the opposite handle (right at the top). You may need to use a thin small screwdriver to move the torsion spring ends into their proper positions. This won't take a lot of force.
Once the handles are together install the pivot screw, T6 torx screw and the hollow screw at the end of the handle. Tighten all three gradually making sure that nothing is binding. Tighten the pivot screw firmly then back it off till the assisted opening feature works well but there is no side to side or other play in the blade.
I haven't used loctite on the screws yet but may if I find them adjusting themselves.
A caution - it appears that Kershaw will provide replacement torsion springs if needed. I'm not sure that taking apart the knife will void the warranty but it is something to consider. Also MAKE SURE THAT THE LOCKING MECHANISM WORKS PROPERLY WHEN YOU ARE DONE.
John.