It looks for two kinds of signals from the phagocyte that has chopped up the microbe. The first signal is the piece of antigen displayed on the phagocyte's surface. The second signal is the all-important danger flag triggered by the pattern-recognition receptors (PRRs) of the cells of the innate immune system. This second signal is essential because it tells the T cells to multiply and ramp up their fighting forces. Without this danger signal, there'd be no serious immune attack.
When an antigen is presented to its matching T cell for the first time, the T cell locks on to an antigen receptor on the phagocyte's surface. This is like a key fitting a customized lock. Binding with the antigen causes the T cell to start making clones -- identical copies of itself that are able to recognize that specific antigen. Where once there was one T cell, over the course of three to five days, a small army of T cell clones comes into being. This army organizes itself into squadrons with assigned tasks. Some are designated to kill infected cells; some activate other lymphocytes to multiply; others, known as memory T cells, remember the antigen and wait quietly for a return visit at a later date.
Because these T cells are so specific, once a T cell recognizes its antigen, it can launch an attack that is tailored to the way that pathogen operates. It anticipates, for example, whether the pathogen will operate inside or outside a cell, and can organize its attack based on that information.