Treated Dirt Coverings
You can cover the area below your deck with treated dirt. Dirt that is treated with salt will be void of vegetation, and will be less likely to retain water. Sprinkle rock salt or sidewalk salt on the dirt below your deck. Allow the salt to settle into the soil. This will prevent tall grasses and weeds from growing through the slats in your deck. It will also be non-toxic if children or pets climb under your deck and play or dig in the soil.
Plastic prevents vegetation from growing under your deck, so you won't need to worry about unsightly weeds poking through the slats. Line the ground with a plastic covering, such as a tarp, pond plastic or landscaping plastic. Dig out about two inches of soil and lay the plastic down. Make sure one end of the plastic is higher than the other so that water can drain off of it. Put the two inches of soil back on top of the plastic. At the base of the slope, create a small ditch that leads away from the deck to drain excess water.
Vegetation and Rock Coverings
If you have a high deck that is open on one end, you will want to take the time to landscape while you cover the areas under your deck. You can use either the treated dirt method or the plastic method to cover under your deck, but instead of simply putting dirt down on top of it, lay down landscaping rocks, plant shallow mosses or place small statues to create a landscaped area. This is especially important if you have an upper deck but people still use your backyard and can see underneath the deck.