I don't normally use a stone unless I've really bunged up the edge breaking out a nick or something. I "Strop" the x-acto blade on a wooden backed leather clad block rubbed with jewelers rouge. Preparing the leather "an old Leather belt piece will work" is fairly simple, contact cement the hair side (smooth side) to the wood block. rub the jewelers rouge cake in the flesh side, working the rouge into the fibres. the leather will gain a shade of white. the rouge is available on-line from www.tandyleather.com
in Texas for about 1.00 /cake.
Stroping strokes are done in reverse of Sharpening stone strokes, pulling the blade backwards over the "flesh side up" Leather. This technique is how we leather workers keep our headknives, and other cutting blades razor sharp for cutting leather in a single efforless pass.
This action removes the factory edge or wire edge created by sharpinging on a stone, making the x-acto blade as sharp as a razor blade without actually removing that much of the metal from the blade. It's more a polishing then shapening. Once this starting edge is obtained, 8 or 10 strokes on the strop each time you pick up the blade will keep is in razor shape.
Part of the trick is to keep the blade at as close to 20 degrees on both sides as possible.
If your looking for scalpel sharpness it will take a lot more time (an hour or so) since you must remove the factory edge angle on a sharpening stone, replacing it with a 20/0 degree taper, that's 20 degrees on one side, 0 Degrees (blade side flat against the stone or strop) on the other. Then stroping to super sharpness.
Sharpening on a stone grinds away the metal of your blade, over a fairly short time you will have ground into the untempered part of the blade. At that point the blade will no longer hold an edge and the blade or knife must be replaced. If your set on using a scarpening stones there are several 3 stone sets that will get the job done, ending with the finial sharpening on a "Hard" Arkansas stone. Remember the consistancy of your angle stokes on stone or strop are very important. varing this angle will make it extremely difficult to get a good edge on your blade. Always use a good sharpening oil on your stones.
I have #1,#2 and #5 X-acto knife handles on my workbench
purchased about 10 years ago that still have the original # 11, 16 and 24 blades. The trick is to strop the blade every time you pick it up. just 4 or 5 storkes per side will keep it super sharp.
Hope this little BSA training helps
OH after using this process Watch your thumbs, NEVER cut anything while your holding it toward yourself or folks will be referring to you a NUBS