On Yom Kippur, at mincha, we read in the Torah about forbidden relationships to remind ourselves that even on the holiest day of the year, we may be subject to temptations and sins.

After Yom Kippur, say the full havdala. 

Note You must light a candle from a flame that was burning since before Yom Kippur began. If you do not have one, skip the blessing on the flame.
If Shabbat coincides with Yom Kippur, you should light the candle from a flame that was burning from before Shabbat began. If you do not have one, you may light a new flame after Shabbat and Yom Kippur are over. Don't say the blessing on spices.

For how to bow at Yom Kippur Musaf Alenu, see Waist-Bowing and Knee-Bowing.

On Yom Kippur (as on Tish'a b'Av), if you must wash your hands to remove:

• Tum'a: You may wash your hands only up to the knuckle that connects your fingers to the rest of your hand (thumb: second knuckle; fingers: third knuckle).
• Dirt from your hand: You may wash wherever the dirt is on your hand.

 

If you must eat a meal including at least 1.3 fl. oz. (39 ml, or 1/6 cup) of bread on Yom Kippur, say birkat ha'mazon afterward. Add ya'aleh v'yavo (and if Yom Kippur coincides with Shabbat, also add retzei).

If you must eat on Yom Kippur (for health reasons), do not make kiddush and do not use two loaves of bread, even if Yom Kippur coincides with Shabbat.

All married men should wear a kittel on Yom Kippur during all prayer services (this is a universal custom). Some men do not wear a kittel during the first year of marriage.

You may not wear leather shoes on Yom Kippur.

Lighting the candles starts the holiday of Yom Kippur.  If you want to start the holiday later, you must:

• Make a condition when lighting candles that you are not yet starting the holiday (by saying “I am lighting Yom Kippur candles but not starting Yom Kippur until 7 minutes before sunset”-this may only be done in urgent situations) and
• Omit the she'hecheyanu blessing at candle lighting.  Men say she'hecheyanu later (in kol nidre).
  Note Women then say she'hecheyanu at least 7 minutes before sunset! (One may not make a condition for she'hecheyanu!)

Yom Kippur fasting starts with candle lighting for women and at least 7 minutes before sunset for men.  

Shir ha'ma'alot should be said after eating a meal that you began after Yom Kippur ended.

On Yom Kippur, it is a universal custom to light one candle if one or both parents are deceased. Every married couple also lights one candle for themselves and their children (if any).

Shir ha'ma'alot should be said after eating a meal that you began after Yom Kippur ended.
See Fast Days.

Shir ha'ma'alot should be said before birkat ha'mazon at the final meal (se'uda ha'mafseket) before Yom Kippur (and also at a meal after Yom Kippur ends).

Yom Kippur is the Day of Atonement. In ancient times, it was more festive than now and unmarried people of both genders would meet and try to find their future spouses.
Yom Kippur is a serious but also a happy day, since all Jews who repent (do teshuva) have their sins forgiven on that day.
Teshuva has four main parts:

• Charata  Regretting what we have done and feeling bad about it.
• Vidui  Recognizing and admitting that we have done something wrong.
•  Kabala  Resolving not to repeat that mistake.
• Azivat hachet  Being in the same situation as before but avoiding doing the sin.

The Torah tells us that there is an inherent property to Yom Kippur that causes spiritual purification and removes sins.
All Jews can become like angels on Yom Kippur.  In order to imitate angels (which are spiritual beings), we abstain from five activities that are associated with physical beings. We do not wash, anoint our bodies, eat or drink, have intimate relations, or wear leather shoes. To further imitate angels, when we say the shema, we say Baruch shem kevod malchuto l'olam va'ed out loud, as opposed to the rest of the year, when we say it quietly.
For more on fast days, see Fast Days.