In fact you are describing a capacitor. A common solution to this problem is to calculate the store energy of the capacitor, which is a function of d . minus gradient of the energy with respect to d is the force:
C=epsilon*S/d , Energy=1/2*CV^2=1/2*Q^2/C=1/2*Q^2*d/(epsilon*S)
therefore F=-grad(Engergy)=-1/2*Q^2/(epsilon*S)
which is an attractive force. The above force can be written in terms of Q, C, and d too, i.e. F==-1/2*Q^2/(C*d)
There is another method which I think is easier to understand. In this method, we find the Electric field due to one of the plates at the position of the other one. Here, ignoring the edge effect, the plates are treated like infinite plates with uniform surface charges. For such a plate, E= sigma/(2*epsilon), where sigma is the surface charge density. See the link below :
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html
Once you have E, you can find Force using equation F=QE , where Q=sigma*S is the total charge of the plate. You get the same equation for the force except that you may have a different sign which depends on which plates are you calculating for and which direction is the positive direction for force. If care is taken, both force become equal.