Although chemicals tackle weeds effectively, you might want to reconsider slathering your garden with them if you have pets or children who run through your yard—or if you’d prefer not to risk poisoning your salad ingredients.
Hgtv.com offers several suggestions for chemical-free weed-killing, including:
Smother weeds with a thick layer of wet newspaper (dampening the paper will keep the sheets together). After the "mat" has blocked the sunlight for a few weeks, the weeds will be dead and the newspaper can be removed.
Pour salt on weeds that sprout up randomly throughout the yard. (This is especially effective for patches of weeds that can't be easily removed one at a time.)
Keep any bare spots (such as those reserved for plants) covered with mulch until it's time to plant; this will prevent weeds from invading the area.