Shabbat is the Jewish term for the Sabbath - the seventh day of the week during which work is avoided to recall G-d resting on the seventh day of Creation - and as such is not a special event upon which certain things happen, as suggested by the question. It is similar in many ways to the Christian Sunday, but falls between nightfall on Friday and nightfall on Saturday.
Many Jews will visit a synagogue for prayers and worship and observant Jews will avoid various activities designated melachot. There are 39 categories of melachot, which is best defined in English as "work" or "deliberate activity" such as lighting fires, driving, operating machinery and so on.
The blessings of the Havdalah ceremony mark the end of Shabbat.
Friday
At a shabbat service at your home or at a synogauge you may light the shabbat candles and say the shabbat blessings. Also some people follow it with hallah and/or a kiddush.
Only in years where Yom Kippur happens to fall on Shabbat (Saturday). Otherwise, no.
They prepare their children for Shabbat and light the Shabbat candles.
"Shabbat Shalom!"
Jews do not call the sabbat "Saturday", it is called 'Shabbat'. Shabbat happens to start Friday at sundown and ends Saturday at sundown, the 7th day of the week.
They're called Shabbat candles (Neirot Shabbat in Hebrew).
In 1998, April 11th was Shabbat and also the first day of Passover. It happens, but not very often.
Shabbat is a time of relaxation, people will read, study, and visit with family and friends.
Shabbat Shabbatot
After Shabbat, there is the Havdalah service.