When lighting Chanukah candles, one should be certain to put in enough oil so that they will remain lit for at least half an hour from the initial lighting time. Similarly, if one is using wax candles, care should be taken that they should be long enough to burn for at least half an hour after the appropriate candle-lighting time which is when stars appear in the sky. There are some multi-colored candles on the market made especially for small Menorahs which do not last for half an hour; one should abstain from using such candles. On Friday afternoon when Chanukah candles are lit earlier than usual, more oil should be added, as will be explained, G-d-willing, in a following Halacha.
On the first night of Chanukah one should light the candle to the extreme right of the Menorah. On all subsequent nights, the new candle should be lit first followed by the candle(s) lit on the previous night(s). Thus, the proper direction for lighting Chanukah candles is from left to right such that the new candle that is added every night due to the additional miracle is lit first.
Our Sages taught us in the Gemara in Tractate Shabbat (23a) that the mitzvah of the Chanukah candles is performed through the lighting of the candles and if the candles are extinguished, one is not obligated to rekindle them. This means that the main Mitzvah is through lighting Chanukah candles which will innately have the ability to burn for half an hour. Therefore, if the candles were extinguished due to a cause non-existent at the time the candles were lit, for instance, if the door or window were opened suddenly and a gust of wind blew out the flames, one is exempt from rekindling the flames. Even so, it is an extra special Mitzvah to relight any candle (without a blessing) that has been extinguished if it is still within a half hour of being lit.
However, if the candle was extinguished before the halachic timespan of half an hour due to an intrinsic reason, for instance, because it was lit in a windy place or it was not filled with enough oil, one is obligated to relight the candle, albeit without a blessing.
One may not derive personal benefit from the Chanukah candles. Thus, one may not use the light of the candles to aid in counting money or reading a book. After the candles have been lit for half an hour, however, one may use the light for whatever one pleases.
It is customary for women not to perform work during the holiday of Chanukah while the candles are lit, i.e. until a half-hour has elapsed from the time the candles were lit. One of the reasons for this is because the miracle of Chanukah was brought about through a woman. This custom should not be treated lightly.