Wet newspapers and put layers around the plants overlapping as you go; cover with mulch and forget about weeds. Weeds will get through some gardening plastic; they will not get through wet newspaper. Good composting!
The newspaper will prevent any grass and weed seeds from germinating, but unlike fabric, it will decompose after about 18 months. By that time, any grass and weed seeds that were present in the soil on planting will be dead. Its green, its cheaper than fabric, and when you decide to remove or redesign the bed later on, you will not have the headache you would with fabric.
how to stop weeds from growing - pull weeds that are there -- then lay newspaper over the entire area --- when covered wet the newspaper real well-- then put mulch on top of that. Ready to plant and be weed free for a year!