Speed wobble, or shimmy, is the lateral oscillation of the head tube and depends largely on frame geometry and the elasticity of the top and down tubes. Shimmy is driven by gyroscopic forces of the front wheel, making it mostly speed dependent.
A common reaction to shimmy while descending a hill is for the rider to firmly grab the handlebars; this moves actually makes the shimmy worse. A looser fitting grip is better at aiding in shimmy recovery.
Many claim the BEST tactic for preventing and recovering from shimmy is to squeeze the top tube with both knees. Keeping one or both knees against the top tube may help in preventing and recovering from this terrifying event.