Keep your broom clean throughout a game, but don't remove debris from your broom so that it falls onto the playing surface.
Keep your body just in front of the moving rock and push your broom back and forth in a straight or slightly diagonal line across and in front of the rock's running surface. Making huge strokes beyond the rock's running surface is wasted effort. Also remember you're sweeping as a twosome, so making large diagonal sweeping strokes in front of the rock can impede your team mate's sweeping ability.
When sweeping it's better not to have your back to the House (The Circle or Rings). If you look towards the House it is safer to see where you are going, what rocks are in play so you don't trip over one, so that you're aware of how far the rock has to travel, and also so that you have an idea of the line that the rock is taking.
Be careful not to sweep so close to the rock that you touch it with your broom. Remember if you do this, or touch the moving rock with any part of your body, your rock is considered "burnt" and is removed from play.