There are eleven paired external intercostal muscles, one on either side of the rib cage.
The external intercostal mm. extend from the tubercles of the ribs posteriorly to the cartilages of the ribs anteriorly, where they end in thin membranes (the anterior intercostal membranes) that continue forward to the sternum.
Each external intercostal m. arises from the lower border of a rib and is inserted into the upper border of the rib below. In the two lower intercostal spaces, the external intercostal mm. do not quite reach the ends of the ribs, whereas in the upper intercostal spaces, the external intercostal mm. extend to the ends of the ribs to the point where their costal cartilages begin.
The external intercostal mm. are thicker than the internal intercostal mm., and their fibers are directed obliquely downward and laterally on the back of the thorax, and downward, forward, and medially on the front (the analogy is "hands in the pockets" - your fingers align with the orientation of the external intercostal mm. fibers when your hands are in your pockets).
These muscles work in unison when inspiration occurs. The internal and innermost intercostal mm. relax while external intercostal mm. contract, elevating the ribs and causing the expansion of the chest cavity, which draws air into the lungs.
The images above show a lateral view of the right half of a rib cage, with the anterior direction to the right of each image.
The external intercostal mm. on the right side are highlighted in blue in the image above. Note that the pectoral muscles have been removed.