Jessica Old Newspapers or cardboard or other natural fibres like old wool carpet. these cut out the light, killing off most weeds and will rot down to allow plant roots to penetrate. Worms will help this process taking the material down into the ground.
Spread the newspapers, cardboard or other natural fibre 3 or 4 deep, over the area you are setting aside for no dig gardening, making sure the materials overlap to smother the weeds, any weeds or grass left uncovered, will grow through the organic matter you are going to spread over the top. Give the ground cover a good soaking and go on to the next stage in preparing for no dig gardening.
Organic material or topsoil, any available organic material will work twigs, leaves, grass cuttings, sawdust, compost from your heap etc. Shovel the organic materials on in layers with the coarsest stuff, twigs etc at the bottom, and the compost or soil on top.
Depending on the area you are going to turn over to the no dig method of gardening you may need more of the organic material than you have available. A little bit of pre-planning may be necessary, ask your neighbours or the local lawn care person for grass cuttings and leaves etc. Providing they are not into composting they will be only too pleased to offload it.