How did the governments - the Union or the Confederacy-go about mobilizing soldiers, citizens, and resources to wage a total war? How successful were their respective strategies?

The Northern states experienced many advantages over their Southern neighbors as the storm of war first released its onslaught across a forlorn garrison of a South Carolina coastal fort. In the North, more railroads had managed to be built than in the South, as the map here shows:

Another example is the vast amount of population differences there were in the North and South. The largest population in the North according to the 1860 census was New York City at 813,699, whereas the largest population center in the South was New Orleans at 168,675 people. (Link)

Again referencing the census, in total population, the Northern twenty-three states outnumbered the South considerably with over twenty-one million people, vs. only nine million in the eleven states of the South, of which more than a third were slaves which they refused to arm to help, fearing insurrections. Because of this, it was relatively easy to replace losses in war in Union units than it was in Confederate ones.

Furthermore, the industrial output of the North was staggering in comparison to the South, including making the vast majority of guns, boots and shoes, cloth, and railroad locomotives, to name a few.

Despite these vast inadequacies, the South had advantages of its own. While they were even outclassed in agricultural capacity by their Northern brethren, they did hold a monopoly on the production of tobacco and cotton, which were in great demand prior to the war. In order to leverage other nations to acknowledge their independence and support them militarily, they used trade to try and make up for the above-mentioned disadvantages of supplies. As the North implemented the Anaconda Plan, blockade running became a lucrative business.

They also were able to take what they needed from the North. As the war began, Federal stockpiles and forts were raided and taken over across the South, and large amounts of the officers from the Federal army, many of them from Southern states, defected to the Southern armies when the war began. Harper's Ferry, a prominent armory and weapons manufacturer since the nation's inception, was also a quick target for Rebel soldiers who sent the machines south to Fayetteville, North Carolina to create their own armory.

For the South, their efforts at searching outward were in vain, as the other nations of France, Spain, and Great Britain shied away from a conflict which quickly was realized to be about slavery, despite the protests of Southern diplomats. Once General Ulysses Grant became head of the Union Army, the South quickly crumbled to a war of attrition, as the north was fueled by a vast domestic base of manpower and supplies.