Odysseus has a simple, yet masterful plan: the bow is placed in his hands by the suitors. His only true help consists of Telemachus and Penelope. They are the ones who institute the test of the suitors: whoever can string Odysseus' bow and shoot an arrow through 12 axe-helve sockets will become Penelope's new husband and King of Ithaca.
Still disguised as a beggar, Odysseus waits as all the suitors (except Antinous, who wants to be the last) try to string the bow; none can. Since no one can, and as a joke more than anything, Odysseus is given the bow for an attempt. He, of course, strings it, passes the test, and proceeds to shoot Antinous in the throat.