How was the union able to gain control of the Mississippi river?

From both ends, from upstream by taking Island Number 10, and then Memphis. From the south by working upstream past Forts Jackson and St. Philip to take New Orleans. Then there was the problem of Vicksburg, Mississippi,which sits atop high bluffs beside the River, on the only high ground adjoining the River in its southern course. Taking Vicksburg required months of effort by the Army, with cooperation from the Navy. Once Vicksburg fell, the last Confederate bastion on the River, at Port Hudson, Louisiana, fell within a week and the Union had complete control of the River, dividing the eastern Confederacy from its west.