Idea #1
Use the newspapers to make paper pots. The pots are biodegradable and relatively easy to make. First gather your newspapers and an appropriately sized can. A soda can or vegetable can will work fine. Whatever size can you choose will determine the size of your pot. Then tear a suitable size strip of newspaper lengthwise. Next lay the can on the newspaper so that long strip of the newspaper will wrap around the rounded parts of the can. Be sure to let some newspaper hang over to cover the bottom of the can. Wrap the newspaper around the can and fold over on the bottom and there is your pot. Fill it with dirt and set it in a flat or a tray so that the pots hold together well. When you water these in the tray do not water the pots themselves, just put the water in the tray and it will gradually seep up to the top of each pot. When you are ready to plant them just bury the pot and all into the ground. It will decay gradually.
Idea #2
Rather than dig up an area to lay a new bed, use newspaper then cover with mulch or dirt. First mow the area as short as you can. Then layer 3-5 sheets of newspaper to make it thick enough to block any weeds from coming up. Cover all gaps between the newspapers (if you don't the weeds will come back). The newspaper and grass will degrade and will help improve the quality of your topsoil. It will take about 4-8 months for the newspaper to degrade. It all depends on how much water the area gets.
You can use this around trees. I like to remove the soil around the trees in a 3 foot circle first. Then leave a small open area around the tree itself, maybe 8"-12" or so. This is so the moisture can easily get to the root ball of the newly planted tree. Then lay the newspaper around the outside of the hole to prevent weeds and cover with mulch! If a weed does pop up, it's usually pretty easy to remove once you've done these hints. I hope you can use this in your garden!