Air plants, true name Epiphytes, are plants native to warm areas such as Florida and Central America, mainly characterized by the fact that they posses no roots, instead absorbing water and nutrients through their leaves. Contrary to their common name, air plants DO NOT live on air, and some species are aquatic, growing on seaweed.
Air plants do not harm their host, instead using it as support. When attached to trees, they grow root-like tendrils to latch themselves in place, which can be safely broken off if harvesting.
The Genus Tillandsia is the most commonly sold, and the type pictured in this instructable. I suggest starting with one of these.
I bought my air plant at Marfield's, an American garden supply chain, for $4.99. That simple. They can also be purchased online, in greater variety, here.