Vicksburg has a municipal airport and is served by Greyhound bus lines.  However, most visitors arrive by car, with Interstate 20 passing right through the city, crossing the Mississippi River and heading out toward Northern Louisiana, Central Mississippi, and beyond.
The nearest large airport is in Jackson, the state capital of Mississippi, approximately 60-75 minutes east of Vicksburg in the center of the state.  Jackson is also served by Amtrak trains, with a full selection of car rental places.
It is useful to have a car in Vicksburg because despite its fairly small, walkable and quaint downtown, the city's attractions and hotels are somewhat spread out at places. The hot weather that Mississippi gets for much of the year also adds to the desirability of having a car.