Relax and Flow: Your stride will naturally elongate going downhill. This overstriding is bad on the level, but going downhill it helps to brake you a bit while gravity keeps you moving faster than usual. If you find yourself going too fast, shorten and/or slow down your steps and keep it natural.
Don't Lean Back: Leaning back will put you off balance, instead stay upright over your hips and knees or lean very slightly forward.
Your Knees: On steeper slopes, keep your knees slightly bent at all times and your torso upright or leaning slightly forward for stability.
Switchbacking: On very steep slopes or those with a loose surface, I like to take a serpentine path and angle for a few steps left, then a few steps right. This switchbacking is a common trail design to reduce steepness either uphill or dowhill.