Proper lighting will reduce the amount of shine on the face but even with the best lighting it can still appear if the skin is oily. As TiagoReil said, good makeup is a necessity. Unfortunately normal makeup doesn't work as well as it should with photographic lights.
The better photographers work with professional makeup artists who have special makeup for photography, and neither the makeup artist or their makeup is cheap.
In your case I recommend you do the following as an absolute minimum.
Buy one of B&H's Impact brand 60" umbrellas for your flash. This large umbrella will give you softer lighting and reduce the size and intensity of reflections from the skin. Position the opening of the umbrella 8'-9' from the subject with the center about face high. A line from the camera to the subject to the center of the umbrella should form an angle of about 35° to 40°.
Place the umbrella opening 90º to the subject, i.e. parallel with a line between the subject and the camera lens. Adjust the position so that the subject is only lit by the back edge of the umbrella. The rest of the face of the umbrella will send soft light onto the shadow side of the face.
http://www.bhphotovideo.com/c/product/423631-REG/Impact_UBBW60_60_Convertible_Umbrella.html
Go to any makeup counter or even to a 7-11 and buy packages of those oil absorbing papers that girls use to blot oil on their faces. Go to a good makeup counter and buy a soft brush and some Clinique Transparency 3 powder. Go to a drug store and buy some rubbing alcohol.
Blot the subject's face with sheets of oil absorbing paper then brush on a very tiny amount of the powder. Keep brushing until you can't see any powder on the face. There will still be enough there to kill the shine but it won't show up in your photographs.
Sterilize the brush between clients by swishing it a few minutes in a jar of rubbing alcohol then air dry it.
CAUTION! Rubbing alcohol is flammable so never do this when smoking or when near an open flame.