The Confederate States of America recognized from the outset of the Civil War that they had disadvantages in terms of population and industrial output. Their strategy was to take advantage of their compact geography, with internal lines of communication, their military heritage (Southerners had been disproportionately the officers of the United States Army), and their greater enthusiasm for their cause to wear down the Union will to wage war. They also believed the Britain, with its heavy dependence on Southern cotton to supply its mills, would be at worst neutral with a bias in their favor, and they dreamed of direct European assistance.
Their specific strategies included privateering in the Atlantic to harass New England merchants with ships like the Alabamaand putting pressure on Washington DC, whose city limits fronted on the Confederate state of Virginia. The South believed that since they did not intend to occupy and hold Northern territory, they would be fighting principally in defense of their homeland and their soldiers would consequently have greater morale and stronger commitment to the cause.
It is interesting to note that the practical objectives which a Confederate victory might have achieved were never greater than what they had in the antebellum situation and which there was little prospect of their losing. Bleeding Kansas had shown they would not be able to introduce slavery into frontier territories, and apart from a few optimists during the secession crisis, there was no reason to believe that the South would enjoy greater prosperity on its own.
America was not inclined to view blacks as equals, and their voting rights in the North were limited. Abolitionism was a minority view even in the North, and many of those who supported the Union cause during the Civil War would not have deprived the South of its "peculiar institution" in peace.
None of this mattered much after South Carolina and the other core secessionists took action. Once Southern states began to secede, the prospects for those who remained began to grow dim as the likelihood of Republican domination of the federal government increased.
In the end, the Southern strategy was to want to win more than the Union did, and this proved to be an illusion.