Even pure water contains $\ce{H2O, OH- and H3O+}$. The two ions can either react with water, or with each other:
$$\ce{OH-(aq) + H2O(l) <=> H2O(l) + OH-(aq)}\tag{1}$$
$$\ce{H3O+(aq) + H2O(l) <=> H2O(l) + H3O+(aq)}\tag{2}$$
$$\ce{OH-(aq) + H3O+(aq) <=> H2O(l) + H2O(l)}\tag{3}$$
All three are fast acid/base reactions. In neutral water, reaction (3) in the forward direction is most unlikely because both reactants are present at very low concentration.
If it's a Bronsted Lowry base then the OH− ions will take H+. But FROM where exactly?
Both reaction (1) and (3) will happen. Because of reaction (3), the $\ce{H3O+}$ concentration will rapidly decrease, making the rate of this reaction very slow. Both reactions (1) and (3) have hydroxide as one of the reactants, but the other reactant is either water (present at high concentration) or hydronium (present at very low concentration in alkaline solution). This makes reaction (1) more likely.
As the OP mentioned, reaction (1) does not use up any water, so that reaction will continue to proceed at a high rate. In fact, some argue that $\ce{OH-}$ is not the best description, and it should rather be $\ce{H2O.OH-}$ or $\ce{H3O2-}$. For the positive ion, $\ce{H3O+}$ is a compromise, acknowledging that there is no "naked" hydrogen ion in water, but not trying to describe higher aggregates.
does the OH– react with the water molecules or with the hydronium ions from the dissociation of water?
The short answer is both.