Screen is one of the best materials to enclose the area under the deck for a number of reasons. It is inexpensive to buy in large amounts and easy to cut and install around the underside of the deck. You will need screws, nails or a staple gun to fasten it in place. You may need to add boards along the bottom of the deck to make this installation process easier. Screen also doesn't seem like an enclosure until you get up close to it. It will also keep mosquitoes from having a safe haven to grow and reproduce, as standing water in a dark cool place, where they live and breed, is often prevalent under houses and decks.
Lattice can be used to enclose the area under decks and can be purchased at most hardware and home and garden stores. Lattice is made of wood or plastic and is quite durable and weather sealed. It is attractive and can be purchased or built to fit in the space under your deck. A problem with lattice is that its holes are big enough to allow bugs and small rodents under your deck, so if this is a problem, lattice may not be the best material to use.
Depending on how big the space under your deck is, building what is known as a deck skirt might be the best solution. Measure the space and cut pieces of wood that match the type and thickness of the wood planks on the floor of the deck. Attach these with screws over the opening beneath the deck from where from the wood planks of the deck end, to the ground This can be done all the way around the deck. It may take more time and money then some of the other options, but it will keep anything from going under the deck.