Organic gardening.

Never mind all the high ideals: do it for selfish reasons. Some people say: "But it's so much more trouble." In fact it's so much less trouble to work with nature than to fight it. Why turn your garden into a battleground -- a battle you can't possibly win? And why poison your food?

"We abuse the land because we regard it as a commodity belonging to us. When we see land as a community to which we belong, we may begin to use it with love and respect."

Aldo Leopold, author of the environmental classic "Sand County Almanac"

And when you apply that lesson in your garden, lo and behold, nature suddenly becomes your friend and ally, doing most of the work for you.
What about pests? Don't you need pest-killers? "The pests are my professors," famously wrote Sir Albert Howard, founding father of the organics movement -- pest attack simply showed him where the soil fertility needed attention. He'd fix it, the pests would vanish. Not just a fairytale -- any good organic grower will confirm it.

It's not just "muck and magic", it's a lot more scientific than trying to kill everything with deadly poisons -- including beneficial predators that kill pests. Healthy plants have good resistance to pests (like healthy people), but they have to be well-fed for that (also like people), and they get their food from the soil (again like people). If it's not in the soil, the plants won't be healthy (and nor will the people). So feed the soil.

The essence of organic growing is soil management and fertility maintenance: feed the soil, not the plant -- the soil will feed the plant very much better than you can.
What's a weed? Same as a pest really: an expert can diagnose an ailing soil's deficiencies and imbalances merely by seeing what weeds are growing in it. They're there for a purpose, well summed-up in the title of a wise book called “Weeds -- Guardians of the Soil” by Joseph Cocannouer.

Fighting weeds is futile. Some grow to cover an exposed soil that's vulnerable to erosion and run-off -- nature hates exposed soil.

So cover it yourself, with a mulch.
Other weeds are deep-rooting plants that go down to the subsoil to collect fresh minerals when the topsoil runs out of them. Composting will fix that -- but leave some of the deep-rooting weeds (herbs actually) growing here and there to open up the soil, your vegetables will appreciate it (so will the earthworms). But they're stealing soil nutrients from your plants? Then your soil is in a bad way! -- certainly not fertile enough for vegetables. Believe the weeds! Tend to the soil and they'll stop pestering you, they'll be easy to manage.

You can find more information on http://journeytoforever.org/