The Planeteers are given their rings by Gaia, the Spirit of Earth, in the first episode of the first season.
Earth: Kwame, from Africa, has the power of Earth. He discovered his ring while planting trees in his home village. The power of Earth can be used to dig trenches, create fire-breaks, prevent landslides, and collapse rocks and riverbanks. Earth is also the first power called to summon Captain Planet, and it would appear to be one of the minimal powers needed for Captain Planet to remain in his solid form.
Fire: Wheeler, from North America, has the power of Fire. He discovered his ring after preventing a street-fight - it was shown to him in a flare of fire from a trash can. The power of Fire not only produces flames, but can be used as a laser-like force to melt locks, cut holes in various materials, and weld materials together. The power of Fire supposedly matches the Planeteer it belongs to: Wheeler can be hot-tempered and impulsive.
Wind: Linka, from the Soviet Union (later changed to Eastern Europe during the opening titles), has the power of Wind. She discovered her ring while playing music to some birds. She can summon miniature tornados with her ring - often blowing away eco-villains with powerful gusts. She can also blow down doors. Linka has also been known to catch people if their fall - and she also has the ability to hover or 'fly' with her ring, though this is draining, and she is unable to continue it for long.
Water: Gi, from Asia, has the power of Water. She can summon up huge tidal waves, whirlpools, and can find water in pipes, drains, or even in plants in the desert.
Heart: Ma-Ti, from South America, has the power of Heart. He can communicate telepathically with people and animals, calming them or asking them to follow directions. In the opening episode, Gaia informs him that this is the most powerful ring of all.
The rings link the Planeteers, as well as allowing them to summon Captain Planet. The rings are weakened by pollution, and will not work at all if there is too much of it around. The rings are also out of action after Captain Planet is summoned, as he is using their powers until he returns to The Cyrstal Matrix.
In the episodes Mission to Save Earth Part I and Mission to Save Earth Part II, five 'opposite' rings are created by Doctor Blight. They can be used to summon Captain Planet's opposite, Captain Pollution.