The Tejana Bracelet tutorial starts with preparing two needles and threading about six feet of thread, divided for ease of handling. The initial step involves picking up six 11/0 seed beads on one needle, adding a Samos Par Puca bead, and crossing the needles through it. This is followed by adding decorative beads on each side of the Samos bead, creating a symmetrical pattern that serves as the foundation for the bracelet's intricate design.