If every collision between reactants lead to a reaction, what determines the rate at which the reaction occurs?

If you assume that every collision leads to a reaction,
then the two main variables affecting the rate of the reaction are the concentration of
the reactants and the temperature.  If the reactants are gases, then the pressure at
which the reaction takes place is also a key variable. Another variable is the use of a
catalyst which can reduce the activation energy needed for the reaction to take
place.

If you increase the concentration of the reactants,
then you increase the probability that the reactants will collide - leading to the
desired product.

Likewise, by increasing the temperature,
you increase the energy going into the system which provides the activation energy
needed for the two reactants to combine to form the desired product. And if the
reactants are gases, the increase in temperature increases their velocity which again
increases the probability that the reactants will collide and form the desired
product.

Keep in mind that for many reactions there is an
equilibrium established between the concentration of reactants and concentration of
products so that every collision in fact does not result in the desired
product.