Make sure that your ground remains filled up with the good stuff. If you leave any portion idle or bare, the weeds are more likely to secure that area for their growth. If you are unable to fill the entire area with plant outgrowths, at least have a good cover to keep the weeds from invading your plant territory.
In the case where weeds have already grown when you discovered them, chopping them off from the ground is the most efficient way to remove them. Some of these weeds may cease to be removed, and will not stop even when you cut them down. But repetitive cutting down of those weeds will help eliminate them for good after some time.
The use of herbicides and pesticides is also advised, but it is not entirely necessary when you are able to do good cultivation of your land. The pesticides and herbicides, especially the commercially available ones, may prove to have other harmful effects. It may also pose as a threat to other useful organisms living in your garden. In any case, when you are presented with a huge weed problem, you may use herbicides and pesticides but only sparingly.
Mulching and composting are also good ways to help maintain the soil and ward off the weeds. Ultimately, you will not have to encounter huge problems in weed management if from the start, you are able to keep them from thriving in your garden in the first place.
If you are really consistent in digging up your space, you will have made the most out of your vegetables' garden and have exercised true growth control against weeds that can steal, kill and destroy your organic garden.