Lasagna (or sheet) gardening is an easy way to start a garden in a new spot or enrich an existing garden. Not to be confused with the Italian dish, this method eliminates the need to work the soil with shovel or rototiller. The reason for the name is because it requires layering of newspapers and compost.
My neighbors used a form of this method for their garden 10 years ago. They mulched with lake seaweed and decomposed chicken manure... it worked well. There were still weeds though and I don't see how you can completely eliminate the need to weed. One of my coworkers uses a weed eater when her garden gets really overgrown. Here's the steps to start a lasagna garden, minus the pasta and weed eater.
1. If you are starting a new garden, pick a spot that will get sunlight most of the day and that will drain well. You don't want your garden in the low spot or the high spot in the yard. Outline the area where you want the garden and mow the grass short.
2. Cover with a thick layer of newspapers, 5 pages thick. Then saturate with water.
3. Next layer with 2 inches of peat moss or other brown organic material such as: leaves, pine needles, straw, rotting hay, composted horse manure or other compost, humus, sawdust, grass clippings, barn litter, coffee grounds, seaweed, paper, cardboard and wood ashes. (whatever you have available).
4. Next layer with 1 inch of green material such as grass clippings, vegetable peelings, coffee grounds, unwanted plants or weeds-that haven't gone to seed. (Fresh grass clippings are high in nitrogen, so don't use very much). It is ideal to use twice as much brown material as green.
5. Continue layering 2 parts brown and 1 part green, as deep as the roots of the plants prior to planting, (usually 8 to 10 inches).
6. Plant the plants, covering around the roots with organic matter. Or... let the raised beds sit and decompose before planting. Either way, give the bed a good saturated watering right away. After planting, continue mulching around the plants as they grow.
In an existing garden, stomp the weeds down or use a weed eater. Then follow steps 2-6 above.