How do you categorize a shareholder? A shareholder is not a supplier or customer so how do you record the payment of a dividend in an incorporated company?

To record a payment to a shareholder you will need to have a G/L account of "Dividends Paid".  This needs to be setup under Owners Equity detail type in the GL.  When you create a check for the shareholder you will allocate the outgoing payment to that GL of Dividends Paid.  

I attached a screen shot of what it could look like to give you an idea.  Hope this helps!