What is the sequence of events that would occur when acid is added to phosphate buffer.?

There are different variations of phosphate buffer, but if we take the one in which NaH2PO4 is in equilibrium with Na2HPO4, then we can write the following:
H2PO4^- <===> H+ + HPO4^2-
When and acid (H+) is added, it will react with HPO4^2- to produce H2PO4^-. Since H2PO4 is a weak acid, it will not dissociate appreciable, thus effectively removing the added H+ from solution and maintaining the pH.