It’s hard to answer that without actually seeing a modern gift economy in action. Luckily, modern gift economies actually do exist. On a small scale, they exist among friends, who might lend each other a vacuum or a cup of flour. There’s even an example of a gift economy on a much larger scale, albeit one that’s not always in operation: The Rainbow Gathering, an annual festival in which about 10,000 people gather for a month in the woods (it rotates among various national forests around the country each year) and agree not to bring any money. Groups of attendees set up “kitchens,” in which they prepare and serve food for thousands of people every day, all for free. Classical economists might guess that people would take advantage of such a system, but, sure enough, everyone is fed, and the people who don’t cook play music, set up trails, teach classes, gather firewood, and perform in plays, among other things.
Check online swap markets and online auctions that have a bartering component such as Craigslist.com (check under "For Sale" for the Bartering category), Swapace.com, SwapThing.com, Barterquest.com, U-Exchange.com, Trashbank.com and Ourswaps.com. Check for local bartering clubs. Your local Chamber of Commerce may be able to provide you with information on similar clubs in your area.
For instance, each time Apple releases a new version of the iPhone, the second-hand market for older versions of the iPhone enjoys a flurry of activity. However, you do have to be as careful with the barter of used goods as you would be with the purchase of used goods. Be sure everything is in working order and shows no signs of significant damage.