For many reactions this question is very easy to answer: the reaction stops when one of the reactants is completely consumed. We say such reactions "go to completion". These are not equilibrium systems. The stoichiometric calculations we learned early in the year are a good model for what happens in these cases. Reactions of this type have fairly negative DGo values, perhaps -100 kJ/mol or even more. We say these reactions are thermodynamically favored since a large negative free energy change is a measure of spontaneity.
That does not mean, however, that such reactions are rapid or even occur to any appreciable extent at standard conditions. The rate of a reaction is determined by the activation energy requirement and the energy available under the reaction conditions. Reactions which are rapid are thus kinetically favored. In this unit we are mainly interested in those reactions which are favored by kinetics but less favored by thermodynamics.
The approach of a reaction to equilibrium can be visualized as a logical result of the collison model for reactions.