How do I make a regular clock motor speed up and/ or run counterclockwise?

Hello sara21, randymc's comment would be true for a battery powered
(DC motor) clock. However, most clocks are powered by your house's AC
electrical system. If you are in the USA, your home power is 120 or
220 volt 60 cycles per second. Your clock motor is what is called a
"synchronous motor". Changing the wires will not change the direction
of rotation. The speed of the motor can only be changed by varying the
60 cycle frequency. Lower frequency the motor runs slower. Higher
frequency and it runs faster. To accomplish this you would need a
variable frequency power supply. Actually if you were to monitor your
home power you would see that the frequency does vary slightly at
different times of the day. Your power company regulates the frequency
so that everyone's clocks don't gain or lose time over a day. If you
are interested I found a very interesting article about the evolution
of clocks:
http://clockhistory.com/telechron/company/documents/warren_1937/

Hope this answers your question.

Redhoss

To make it run counterclockwise, reverse the wires from the power source.

I'm not sure there is a regular clock motor. At least 5 designs are in
common use. I don't think any in common use run backwards if you
reverse the battery.
 You can buy a box (for a few hundred dollars) that produces 120 volts
ac at adjustable frequencies from a few hertz to about 400 hertz that
will run the type of plugin clock popular 1935 to 1980 (over part of
that frequency range) A few of this old type of electric clock are
still made for 50 hertz and most of them will run 20% fast if you
operate them on 60 hertz.
 The local power company needs to disconnect from the North American
grid to change frequency even a few parts per million. I suppose
someone in each region, instructs specific power plants to lead or lag
the grid phase by about one degree to keep the frequency of the grid
plus or minus a few parts per billion.
 Some clocks have a fast/slow knob or lever, but the adjustment
possible is probably smaller than you had in mind.
You could cut a big hole in the clock case remove a few gears and
replace them with a different gear train mounted outside the case. Few
people have the know how to design a external gear train that would be
reliable, and chances of being able to find an an already made train
that will do the job are extremely unlikely.
 Generally it is not practical to make clocks run backwards or at
different speeds, except at a clock factory where it could be done for
a few thousand dollars whether we make one or several thousand of
these strange clocks.   Neil

You might try to find an old "non-self starting" clock.  These are
restarted after a power failure by spinning a starting knob.  If spun
backward, the clock will then run backward, until the next power
failure.
  I believe that the self starting synchrous motor was invented about
1920, so you would search for an electric clock built before 1920. 
You would be wise to have the power cord replaced before pluging the
clock into your wall socket, because these old power cords were just
wrapped in cloth, which will probably have rotted.
  The motors used were synchronous, so the speed will be the same, but
in the wrong direction.
  I was able to purchase one of these clocks for about $20 dollars on
Ebay.  The power cord had already been replaced on mine, and this
beautiful old clock runs perfectly.
Jay