Because the timing of Shabbat depends on natural occurrences (sunset, the appearance of three stars), the exact beginning and end times differ from week to week and place to place.
Shabbat is the seventh day of the Jewish week and a day of rest, mimicking G-d's period of rest after creating the world, which can be celebrated at home or with the larger community. It begins at sunset on Friday and is traditionally ushered in with a candle-lighting, a kiddush blessing over and drinking of wine or grape juice, and a blessing over and eating of braided challah bread before a festive meal. Some also sing other special songs and prayers.
During the day Saturday, any form of "work" is prohibited. Depending on one's level of observance, this can include driving a car, using any form of electricity, handling money, cooking a meal, or even carrying something from place to place (Indianapolis does have an eruv, or boundaries within which items may be carried). These rules are designed to allow more time for "leisure" activities like attending synagogue services, reading, enjoying a (pre-prepared) meal, conversation, spending time with family and friends, singing, taking a nap, taking a walk, or studying Torah.
Shabbat ends on Saturday night, after three stars have appeared in the sky. Some observe the ending of Shabbat and beginning of a new week with a havdalah (division, separation) ceremony: lighting a braided candle, a blessing over wine or grape juice, and smelling fragrant spices.