The only way to kill weeds permanently in a large area is to make the soil completely hostile to all plant growth. Since you probably want to kill weeds to make way for a new lawn or garden, an environmentally friendly weed-killing approach is the way to go.
Block All Sunlight
One of the best ways to kill weeds in a large area is to smother it with a material that won't let any light filter through. Without sun exposure, the plants will be unable to create energy through photosynthesis. Weeds will use energy stored in their roots to make a last-ditch effort to break through your barrier and reach the sun, so be sure to use a sturdy material like a black tarp, several layers of thick cardboard or landscape fabric and create a tight seal around the edges with bricks or garden staples.
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Best of all, this method allows you to suppress weeds while growing desirable plants in the same area. Just cut an "X" through your barrier to reach the dirt, dig a hole and plant what you'd like to grow. Use garden staples to press the barrier into place, leaving enough room around the stem to allow water to reach the plant's roots.
Disturb the Weeds' Roots
Weeds are survivors. Anyone who has tried to pull up a dandelion, for example, knows that it's pointless to remove the leaves if you don't also remove the entire root. The barrier method will work as long as the barrier stays in place. Once you remove it, such as to plant grass, some of the hardier weeds will sprout from the roots still in the soil.
Even if your future landscaping plans don't require you to till or aerate the soil, doing so will disturb the weeds' roots. Without good contact with the soil, the roots will not be able to absorb water, oxygen or nutrients. Most will die as a result. Still, it's a good idea to remove any roots that come to the surface to permanently remove them once and for all.
Plant and Nurture the Competition
If you plan to sow grass seed after killing the weeds, do it immediately after removing the barrier and/or tilling the soil. Exposed soil will be extremely susceptible to weed infestation if any weed seeds land on it, so you want the grass seed to have a head start. Grass seed will germinate even sooner if you soak it first.
If you previously tried to grow a lawn and it was overtaken by weeds, try to figure out what went wrong and make appropriate modifications. Test the nutrient content and pH of your soil, for example, and make sure you choose the best type of grass seed for the site.
Kill New Growth Immediately
Regardless of what you have planned for the area, there will be some weeds along the way. The key is to kill new growth immediately before it has a chance to smother or compete with your desirable plants. Use a tool like a garden knife to dig out weeds by the root if needed.
As long as there is no mulch or dry plant material nearby, you can also use a torch to kill weeds (it's great for killing weeds in patio cracks too). Other methods, like pouring boiling water or vinegar over the weeds, may also kill grass or garden plants, so proceed with care.