During the winter of 1862, Grant tried to find a way around Vicksburg. He tried four "experiments" as he called them, but none worked. During those failed experiments he learned it was easy to forage through the South and live off their food supplies.
Grant then had an idea, he would try to march around and take Vicksburg from the south. He went down the West Side of the Mississippi River through Louisiana to Hard Times. He tried ferrying across the river to take Grand Gulf but that didn’t work. Then he learned from a slave that there was a crossing nine miles down the river. It turned out the crossing was not even defended. The Confederates did not have enough men to defend everywhere and Grant had faked an attack on Vicksburg so the Confederates had moved men up to defend the city while Grant crossed to the south.
Once on the other side of the river he marched northeast toward Jackson and took that fort and town before turning west to Vicksburg.