all you really need to know is this:
- strong base + strong acid: equivalence point at pH = 7
- strong base + weak acid: equivalence point at pH > 7
- weak base + strong acid: equivalence point at pH < 7
- weak base + weak acid: who knows?
i'll explain what happens when you mix strong acid with strong base. the explanation for the others is pretty much the same.
e.g. NaOH(aq) + HCl(aq) --> NaCl(aq) + H2O(l)
when equivalence point si reached, in the vessel you would have: Na+(aq) ions, Cl-(aq) ions, a bit of H3O+(aq), a bit of OH-(aq), and heaps of H2O(l) acting as the solvent.
now Na+(aq) has no acid-base properties so its presence does not effect the pH of the solution. Cl-(aq) can function as a base, but since it is the conjugate base of a strong acid, it is a pathetic base, and so we can safely ignore it. so the only species that will affect the pH are H3O+(aq) and OH-(aq) from the self-ionisation of water. we know that at 25 degrees celsius, Kw = 1.00 * 10^(-14) M^2. so [H3O+] = [OH-] = 1.00 * 10^(-7) M. so we have pH = -log_10[H3O+] = -log_10(10^(-7) = 7.
now remember how we discounted Cl-(aq) because it's the conjugate base of a strong acid? well, when you mix a weak acid and a strong base, the corresponding anion would be the conjugate base of a weak acid, making it a weak base (not a base of negligible strength anymore). so its presence would affect the pH of the solution. in fact, its presence will increase the pH. so at equivalence point, pH > 7.
for weak acid + weak base, it's a bit more complicated, because you aside from the hydronium ions and hydroxide ions produced by the self-ionisation water, you have a weak base AND a weak acid.