How did war between the north and south end?

It ended with a peace treaty between the North and South . In early 1865 the Confederates had tasted defeat and tried to negotiate for peace between the "two countries", but Lincoln could accept nothing short of Union, and the Southerners could accept nothing short of independence. So, the war kept going. The end came swiftly with the advancing Northern troops capturing Richmond and cornered Lee at Appomattox Court House in VA in April 1865. Grant met with Lee on Palm Sunday and granted generous terms for surrender. Among the concessions was that the hungry Confederates could keep their horses for spring plowing. The worn out tattered Confederate troops weeped as they took leave of Lee. The elated Union troops cheered, but were silenced by Grant with "The war is over; the rebels are our countrymen again."