How the civil war came to an end?

Grant ended the system of prisoner-exchange, so the Confederates were bound to run out of manpower. After he cornered Lee at Petersburg, he had only to wait for this to happen (though it was quite a long wait, with high casualties that could have cost Lincoln his re-election in November 1864.)

Meanwhile he ordered Phil Sheridan to lay waste to the fertile Shenandoah Valley, bread-basket of the South, and allowed Sherman to wreck the farms and railroads of Georgia, further helping to starve the Confederates armies in the field.