Applying a 3-inch-thick layer of organic mulch will go a long way toward suppressing weeds. It also provides nutrients for plants as worms and other soil-dwelling creatures break it down. Use bark dust, wood chips, straw (not hay, which contains weed seeds), pine needles or shredded leaves. Dry grass clippings, built up slowly in thin layers, also work well. Don't put a thick layer of freshly cut grass down, or it will rot and smell.
Weed barriers come in rolls or by the foot at nurseries. They are made from cloth or plastic and are easiest to use for pathways or when starting a new garden. To use them in a bed of established plants, cut the material into strips or blocks and fit it around the plants. Cover it with at least an inch of organic mulch. UV-resistant polypropylene fabric lasts longer than other blockers.
Cardboard, newspaper, kraft paper and brown grocery bags make effective weed blockers when overlapped thickly under organic mulches such as wood chips or compost. Although they decompose in about a year, they are easily available, cheap and effective. Since most gardeners reapply mulch yearly anyway, this can be an easy way both to nurture plants and suppress weeds. Black ink no longer contains lead, a past concern about using newspapers, although colored inks may.
Black plastic is good at suppressing weeds, but unless completely covered by a thick layer of mulch, it breaks down into shreds when exposed to sunlight. This makes it difficult to remove if you change your mind about the garden layout. Because it is nonporous, it doesn't let water or air through to the ground, so soil beneath it becomes compacted and dry. While it may work well for a permanent pathway, it isn't a good choice for a garden area.