The following short video by Chabad.org provides a wonderful brief overview of the Story of Hanukkah.
How Hanukkah Is Observed
On Hanukkah we light the menorah (an eight-branched candelabrum, also called a hanukkiah) each night at sunset, and recite a blessing. On each successive night we light an additional candle, using a ninth candle, the shammos (the center candle, mounted above the others) to light each one. This is to fulfill a prohibition that we not light Hanukkah candles using other Hanukkah candles. Jewish scholars have long considered the lighting of the candles a sacred act. Maimonides writes:
“The commandment to light the Hanukkah lamp is an exceedingly precious one, and one should be particularly careful to fulfill it, in order to make known the miracle, and to offer additional praise and thanksgiving to god for the wonders which He had wrought for us. Even if one has no food to eat except what he receives from charity, he should beg—or sell his garment to buy—oil and lamps, and light them.”
During Hanukkah we also give gifts and sing songs. See “Customs and Folklore” below for more on the observance of Hanukkah.
Source: Jews for Jesus