In my own asparagus patch, for example, I have kept weeds out for many years with an annual mulch of salt hay. The hay, available in bales at nurseries, decomposes with time and adds to soil fertility. Mulching takes many forms, one of the most drastic being to lay down heavy layers of newspapers, building paper or both where you seek to eradicate unwanted growth. Black plastic may also serve. It takes several weeks to kill everything, provided no light leaks in.
Dead leaves make good mulches in flower beds or among vegetables as do wood chips.
You can make your own chips with gasoline-driven or electric chippers and you can also buy bags of them. Sometimes a road crew will give you a big mound of them when they cut down tree limbs and put them through big chippers on the spot. In our environmentally conscious era, many gardeners think twice before resorting to chemical weed killers, called herbicides, because of real or feared harmful effects. But, when properly used, herbicides do a fine job. Some are selective, meaning they re aimed at killing specific plants, while others, nonselective, will kill a broad range of plants.