Hanukkah commemorates a miracle involving oil. This explains why we eat oily foods to celebrate. Some eat fried potato pancakes (latkes), others eat sufganiyot—fried doughnuts. Some eat both. Most survive the holiday.
Yes, food can be dangerous. One of the greatest Maccabean victories resulted from feeding the enemy cheese, which is why we also eat dairy foods during Hanukkah.
Hanukkah money
During Hanukkah it is customary to give money to children, to teach them to give tzedakah (charity), and to maintain a festive and joyful spirit.
Dreidel
The Greek oppressors banned Jewish schools, so the children had to study in the woods, with sentries posted to warn them of Greek patrols. When an alert came, the children hid their schoolbooks and played with the dreidel (spinning top).
We also play on Hanukkah to commemorate the courage of those children. The four Hebrew letters on the dreidel correspond to the words nes gadol haya sham (a great miracle occurred there), so playing the dreidel reminds us of Hanukkah even in a moment of fun.
The prayer
Each day of Hanukkah, we thank God by reciting the entire Hallel (a series of psalms) in the morning. We also insert a special prayer of thanksgiving, ve'al haNisim, into the blessing after meals. Each morning, we read from the Torah about the dedication offerings brought in the desert for the dedication of the Tabernacle (Mishkan), in remembrance of the rededication of the Temple by the Maccabees.
Shabbat Hanukkah
On Friday afternoon, the menorah is lit before the Shabbat candles. On Friday night, the Hanukkah candles must burn for at least half an hour after nightfall, so more oil is added, or longer candles are used. On Saturday night, the menorah is lit after Shabbat and the Havdalah ceremony have concluded.