A titration is a chemistry experiment where you drip -- "titrate" -- one substance into another using a glass tube (burette) and a beaker. In an acid-base titration, you titrate a base into an acid until it reaches its "equivalence point," or a neutral solution with a pH of 7. Before this occurs, the solution in your beaker is a "buffer solution," one which resists changes in pH when you add small amounts of acid. You can represent the extent to which your acid dissociates -- and thus changes the solution's pH -- using its "pKa" value, and you can calculate this value using data from your titration experiment.
Pick a point on your titration curve prior to the equivalence point and record its pH, which is the vertical coordinate of the curve. For example's sake, suppose you're analyzing a solution at a point when its pH is 5.3.
Determine the ratio of the acid to its conjugate base at this point, keeping in mind the volume you need to add to reach the equivalence point. Suppose you needed to add 40 mL to reach the equivalence point. If, at the point when the pH is 5.3, you have added 10 mL, it means you are one quarter of the way to the equivalence point. In other words, three quarters of the acid still needs to be neutralized, and the acid's conjugate base accounts for one quarter of the solution at this point.
Plug your values into the Henderson-Hasselbalch equation, pH = pKa + log ([A-]/[HA]), where [A-] is the concentration of conjugate base and [HA] is the concentration of the conjugate acid. Keep in mind that since you've measured pH as a function of the titrant's volume, you need only know the ratio of conjugate base to acid. At the point when the example solution had a pH of 5.3, this was (1/4)/(3/4), or 1/3: 5.3 = pKa + log (1/3) = pKa + -.48; so 5.3 + .48 = pKa + -.48 + .48, or pKa = 5.78.