I am not the first to make a chair out of a shopping cart; google it and you can see a lot of possibilities. So, I approached the problem with a mind towards simplicity, making just a few precise interventions. It took me less than two hours to make. Tools are minimal: an angle grinder with a metal cut-off wheel, a dremel or equivalent, or even bolt cutters, two pieces of scrap wood, and two clamps. A drill could come in handy depending on the condition of your shopping cart.
The chair is really comfortable: the front wheels elevate the front of the seat and create a nice recline. The seat is deep and roomy, and the arms are wide, at a low height. Since shopping carts are made to sit out in the weather, this could be an indoor/outdoor chair. With the handle intact and the wheels in the front, it is easy to lift a little and wheel around. On my flickr page here, you can see another shopping cart chair a buddy and I made, with a shopping cart chassis and some oven grates.
I found mine in an alley, missing its front wheels. I think, as an experienced dumpster diver, you have to make a judgement call on things. I would recommend taking a cart only if it is nowhere near a relevant supermarket or other store and/or it is somehow damaged but salvageable for our purposes. Other possible places to get carts are the local/county dump, private metal scrap yards, craigslist, stores going out of business, or asking at a store what they do with damaged carts. Shopping carts are apparently quite expensive for retailers to purchase, and they expect them to last a long time. Don't steal carts.