In intaglio printmaking, you make marks on the matrix (in the case of aquatint, a copper or zinc plate) that are capable of holding ink. The inked plate is passed through a printing press together with a sheet of paper, resulting in a transfer of the ink to the paper. This can be repeated a number of times, depending on the particular technique.
Like etching, aquatint uses the application of acid to make the marks in the metal plate. Where the engraving technique uses a needle to make lines that print in black (or whatever colour ink is used), aquatint uses powdered rosin to create a tonal effect. The rosin is acid resistant and typically adhered to the plate by controlled heating. The tonal variation is controlled by the level of acid exposure over large areas, and thus the image is shaped by large sections at a time. Another tonal technique, mezzotint, begins with a plate surface that is evenly indented so that it will carry a fairly dark tone of ink. The mezzotint plate is then smoothed and polished to make areas carry less ink and thus print a lighter shade; or, beginning with a smooth plate, areas are roughened to make them darker; or, these two techniques may be combined.