Hanukkah is not a very important religious holiday. The holiday's religious significance is far less than that of Rosh Hashanah, Yom Kippur, Sukkot, Passover, and Shavuot. It is roughly equivalent to Purim in significance. Hanukkah is not mentioned in Jewish scripture; the story is related in the book of Maccabbees, which Jews do not accept as scripture.

The only religious observance related to the holiday is the lighting of candles. The candles are arranged in a candelabrum called a menorah (or sometimes called a hanukkiah) that holds nine candles: one for each night, plus a shammus (servant) at a different height. On the first night, one candle is placed at the far right.

The shammus candle is lit and berakhot (blessings) are recited. Every night during Hanukkah, when the candles are lit, these two prayers are recited:

Ba-ruch ata, A-do-nai E-lo-hei-nu, me-lech ha-o-lam, a-sher ki-de-sha-nu be-mits-vo tov, ve-tsi-va-nu le-had-lik neir shel Han-nu-kkah.

Ba-ruch ata, A-do-nai E-lo-hei-nu, me-lech ha-o-lam,she-a-sa ni-sim las-a-vo-tei-nu ba-ya-mim ha-heim ba-ze-man ha-zah.

On the first night only, add:
Ba-ruch ata, A-do-nai E-lo-hei-nu, me-lech ha-o-lam, she-he-chya-nu ve-ki-ya-ma-nu ve-hi-gi-a-nu las-man-ha-zeh.

After reciting the blessings, the first candle is then lit using the shammus candle, and the shammus candle is placed in its holder. The candles are allowed to burn out on their own after a minimum of 1/2 hour. Each night, another candle is added from right to left (like the Hebrew language). Candles are lit from left to right (because you pay honor to the newer thing first). On the eighth night, all nine candles (the eight Hanukkah candles and the shammus) are lit.

Why the shammus candle?
The Hanukkah candles are for pleasure only; we are not allowed to use them for any productive purpose. We keep an extra one around (the shammus), so that if we need to do something useful with a candle, we don't accidentally use the Hanukkah candles. The shammus candle is at a different height so that it is easily identified as the shammus.

It is also traditional to eat fried foods on Hanukkah because of the significance of oil to the holiday. Among Ashkenazic Jews, this usually includes latkes.

Gift-giving is not a traditional part of the holiday, but has been added in places where Jews have a lot of contact with Christians, as a way of dealing with our children's jealousy of their Christian friends. It is extremely unusual for Jews to give Hanukkah gifts to anyone other than their own young children. The only traditional gift of the holiday is "gelt," small amounts of money.

Another tradition of the holiday is playing dreidel, a gambling game played with a square top. Most people play for matchsticks, pennies, M&Ms or chocolate coins. A dreidel is marked with four Hebrew letters: Nun, Gimmel, Heh and Shin.

This supposedly stands for the Hebrew phrase nes gadol hayah sham, a great miracle happened there. Actually, it stands for the Yiddish words nit (nothing), gantz (all), halb (half) and shtell (put), which are the rules of the game! There are some variations in the way people play the game, but the way I learned it, everyone puts in one coin. A person spins the dreidel. On Nun, nothing happens; on Gimmel (or, as we called it as kids, "gimme!"), you get the whole pot; on Heh, you get half of the pot; and on Shin, you put one in. When the pot is empty, everybody puts one in. Keep playing until one person has everything. Then redivide it, because nobody likes a poor winner.