Weeds are plants growing in the wrong place or my favourite definition - any plant whose virtues have not yet been discovered.
You can pull weeds all out by hand or hoe them or you can just remove the ones that are most probematic for your plants. The right weeds can help keep the soil moist around your plants like a mulch and will add organic matter in a similar way to green manures.
Using weed killer has already damaged so much of the environment.
A no-dig garden approach with regular mulching will eventually suppress weeds.
Weeds like any plant will be weaker if they are in the shade. Once plants are established the problem of weeds does diminish. Intercropping with two different plants will minimise the space and light that weeds have. Succession sowing will stop the ground being empty for long periods of time.
Cover crops and improve drainage and can be a good source of nutrients when dug back into the soil. While the crop is growing weeds will be suppressed.
'One year's seeding makes seven year's weeding'. Try to remove weeds before their seed heads have developed. Learn to recognise weed roots as you dig. Pull on weeds gently to try to remove as much of their roots as possible.
Cut the leafy growth from weeds after flowering before the seeds set. The cuttings can be put on the compost heap. Constant cutting will weaken the weed and eventually it will die. This is a good way to weed around your plants to minimise root disturbanace. Hoeing with a sharp tool will cut just below the soils surface.
Cooking the weeds under plastic. This is useful for ground clearance on a patch that has been neglected. Try to borrow from someone rather than buying any yourself. Plastic sheeting can be reused many times. A better method is to lay down cardboard or newspaper and cover with a layer of mulch.
Rotavators and digging without taking the weed roots out will actually increase your problem. Rotavators chop weed roots into small pieces and some weeds for example bindweed and nettles will grow from the tiniest piece.
One of the things that I was horrified to see when we first had our allotment was the willingness of some allotmenteers to resort to weedkiller.
There are alternatives and I admit they will never work as well as chemical weedkillers.
Here are some recipes to try:
3 parts vinegar to 1 part Castile soap sprayed onto the leaves will kill the plant but not necessarily the taproot permanently.
Distilled white vinegar can also be added directly on top of the weeds.
Use for paths or cracks in paving. Pour on a layer of salt and water gently or apply just before rain to let the salt soak into the soil.
Disolve one cup of salt in a litre of water. Paint onto the weed you want to kill.
This will kill weeds and their seeds.