This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
How do you quickly solve Rubik's clock?
Solution to Rubik's Clock
The solution to Rubik's Clock is very simple and the clock can be
"worked" in 10-20 seconds once the solution is known.
In this description of how to solve the clock I will describe
the different clocks as if they were on a map (e.g. N,NE,E,SE,S,SW,W,NW);
this leaves the middle clock which I will just call M.
To work the Rubik's clock choose one side to start from; it does
not matter from which side you start. Your initial goal
will be to align the N,S,E,W and M clocks. Use the following algorithm
to do this:
 Start with all buttons in the OUT position.
 Choose a N,S,E,W clock that does not already have the
same time as M (i.e. not aligned with M).
 Push in the closest two buttons to the clock you chose in .
 Using the knobs that are farest away from the clock you chose in
 rotate the knob until M and the clock you chose are aligned.
The time on the clocks at this point does not matter.
 Go back to  until N,S,E,W and M are in alignment.
 At this point N,S,E,W and M should all have the same time.
Make sure all buttons are out and rotate any knob
until N,S,E,W and M are pointing to 12 oclock.
Now turn the puzzle over and repeat steps - for this side. DO NOT
turn any knobs other than the ones described in -. If you have
done this correctly then on both sides of the puzzle N,S,E,W and M will
all be pointing to 12.
Now to align NE,SE,SW,NW. To finish the puzzle you only need to work from
one side. Choose a side and use the following algorithm to align the
 Start with all buttons OUT on the side you're working from.
 Choose a corner that is not aligned.
 Press the button closest to that corner in.
 Using any knob except for that corner's knob rotate all the
clocks until they are in line with the corner clock.
(Here "all the clocks" means N,S,E,W,M and any other clock
that you have already aligned)
There is no need at this point to return the clocks to 12
although if it is less confusing you can. Remember to
return all buttons to their up position before you do so.
 Return to  until all clocks are aligned.
 With all buttons up rotate all the clocks to 12.