Fly to Veilstone City and head to the Team Galactic HQ. You'll need to find a Storage Key (found in the Team Galactic Warehouse) to enter. Navigate through the maze-like building, battling Grunts and scientists. You'll eventually find Commander Saturn and then Cyrus, the leader of Team Galactic. After defeating Cyrus, he'll activate his plan. You'll then need to head to Mount Coronet (fly to Celestic Town and head east). Navigate through the upper sections of Mount Coronet, using Rock Climb (if you have the badge) and Surf. You'll eventually reach the Spear Pillar at the summit.
