Answer: There are several methods you can try, and most gardeners use them in combination. First of all, the soil contains a huge number of old weed seeds and these will germinate if brought to the surface, so reducing the amount of soil disturbance can reduce the weed seedlings. You might find that using a preemergent treatment of corn gluten meal helps with some weeds, including crabgrass. (Disturbing the soil will break the barrier, so this does not work everywhere, but can be great in paths.)
Next, a light scuffling or hoeing can stop many germinating seeds right at the start. Doing this once or twice early in the season can help greatly. Then, apply an organic mulch several inches thick to smother any additional seedlings.
Should any weeds make their way up through the mulch, you could pull them, repeatedly hoe them off to exhaust their root reserves, or smother them by piling more mulch on top of them.
Smothering can be very helpful if you have persistent weeds such as dandelions. Clip off the foliage, then cover the weed with several layers of newspaper and a thick layer of mulch. Excluding the light will keep it from re-emerging.
Next in the arsenal is making sure no weed goes to seed in the garden or in nearby lawns or fields if at all possible. This may mean mowing the perimeter area.
When adding soil amendments and/or mulches, be aware of weed seeds. Horse manure is notorious for importing weed seeds, as is hay mulch. These should be composted in a hot pile. Straw mulch is less prone to weed seeds. Leaving any area fallow is an invitation to nature to plant it, so make sure to use cover crops whenever possible, these will also help build your soil.
Finally, reducing the area you need to keep clear can save you a lot of time. You might consider using matted rows and/or slightly raised beds to make the most efficient use of space. Growing the veggies on a tighter spacing also crowds out weeds by acting as a groundcover of sorts.
I hope this gives you some ideas. You should also be heartened by the thought that the first year is the worst for weeds, each succeeding year after that should be easier.
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