Lay the corrugated cardboard or wet newspaper (a dozen sheets thick) directly onto the ground. Yes it's perfectly fine to just cover those weeds. Overlap each piece at least 3 inches.
Tip: Use only black and white newspaper. Save the glossy sheets for the recycling bin as these may contain chemicals that aren't good for plants.
Spread 3-4 inches of organic mulch on top. This can be grass clippings, compost, straw, leaves, weed-free hay, or even pulled weeds that haven't set seed. Allow at least 1-2 inches of breathing room around each of your plants.
Not only will the mulch smother the weeds, it will also improve your garden soil as it breaks down adding yummy nutrients for your plants. Add additional mulch as needed every few months.
According to Patricia Lanza,
"...you can create lush, successful, easy-care gardens in practically any location without hours of backbreaking digging or noisy tilling."
For lots of time-saving tips, check out her book at: