The short answer is that you hold the smudge feather (or smudge stick if not using a feather) in the hand with which you send (project) outward when performing a clearing, and probably any other spiritual practice involving moving energy, thought or intent.

Some people project energy with their dominant (strongest) hand while others use their right hand (whether they are right-handed or left-handed) because their tradition is that energy flows in (is received) from the left and sent out through the right. It may be that some people project from either hand. Here are suggestions for determining your projecting hand.

• Pretend you have an urgent need to stop an attack of some kind. Throw your hand up in front of you and shout, "Stop!". The hand you raised unconsciously is the hand you project with. Your body and inner self already know which hand will send your command with swiftest, clearest intent.
• Sit quietly for a few moments. Imagine that a beautiful butterfly has come light upon you. The butterfly rests on your lap, stomach or chest and softly spreads its magnificent wings. Imagine sitting with the butterfly for as long as you like. When you are ready, make the inner decision to release the butterfly into the sky with love and appreciation, letting it know that you are sending it out into the world to share its beauty and inner messages with others. Gently place your hand in front of, then underneath the butterfly, and allow it to climb upon your open palm. Then, with one swift; but gentle motion, launch the butterfly up into the air with kindness and affection and observe it glide up into the sky. Which hand did you use tos send the butterfly into the world?