They are not opposites, but complementary. In Classic Chinese thought, Yin is the femininine, passive, receptive, nurturing, moist, earth force; and Yang the masculine, active, energetic, creative, dry, sky force (I add that this does not mean women and men, because we all have yin and yang in us). In order for anything to exist, you need the pairing of yin and yang - just as you need a male and female to make a baby (in most species). They are often replaced by "Earth and Sky", as a pairing.
You can read up on them in any good I-Ching book, since they are at the heart of the hexagrams. The first hexagram of the I-Ching is called the Creative, and is the pure Yang force - representative of the Sky (as symbolised by the dragon). And the second is called the Receptive, and is the pure Yin force - representative of the Earth (as symbolised by the mare). Throughout all the remaining 62 hexagrams, you see them combined in varying ways, and the value of one or the other or both together put forward. When they don't work well together that's when things go wrong - you get an "arrogant dragon" or a passive-aggressive yin.
