Here are two good ways you can recycle in your garden: composting and mulching with newsprint.
Kitchen waste (fruit and veggie peels and non-seed parts, egg shells, tea leaves, etc.) can be mixed with yard waste (grass clippings, broken up tree branches, leaves, dried up flowers) and newsprint (non-slick pages) to make a great nutrient booster for your plants and trees. You can build your own compost bin, or buy one. The city of Chicago periodically has them available for Chicago residents at a subsidized price. Look for announcements in the local papers (usually in spring) or on the city's Dept. of Environment web page.
I got one of the city bins last summer. It got a slow start. I found that the compost needed to be turned regularly (once a week or more) and needed a certain level of moisture for things to decompose quickly. Turning the pile with a pitchfork or hoe or shovel can be challenging unless you have a fair amount of upper body strength. When I got a compost turner tool, it made the job a LOT easier (5 minutes with the tool, compared to 20-30 minutes with a shovel) and speeded up the process of decomposition by about 5 times. One trick I learned was to rinse the tool afterwards to keep it from getting clogged. I do this over the bin, adding moisture to help the materials rot.
When I pull weeds, I hold a bunch together and cut them with scissors before adding them to the compost bin so that they rot quicker. I crumple dry leaves up and break or cut small branches into pieces. Whatever you add rots faster if you shred it or break it into smaller bits. This is true for newsprint as well. BTW, the newer inks now used in newsprint are often soy-based and generally use non-toxic pigments, unlike the inks used years ago.
One warning: do NOT include seeds when you're adding to your compost bin. Unless your compost gets really hot, it will not kill the seeds, and you'll be spreading them wherever you spread your compost. If seeds are from an invasive weed, it could get everywhere fast.
Now that the compost is rotting fast, I've got a ready supply of black gold for the garden. My strawberries had stopped producing at the end of June. I put compost around the base of each plant and watered well. Within a week, the plants had new flowers on them. Now I'm eating strawberries again. Plants that were looking so-so are doing a lot better with the addition of compost. Of course, regular watering is a key piece of the equation.
You can use newsprint as mulch. Lay 3 or 4 sheets over an area, either around existing plants or poking holes where you'll plant new ones. It helps keep weeds from getting light to grow. You can add a light layer of damp leaves or bark mulch on top to hold it down and make it look nicer. Use a thicker layer of newsprint to kill grass in areas where you want to later remove grass for new flower or veggie beds.
Newsprint can also be used to make starter pots for seeds.
It's cool to be able to recycle and grow things at the same time.