The South had a number of strategies:
1) The First strategy was to try and take the White House as fast as possible. This was almost made possible with both Battle of Bull Run, but overall failed in taking the White House. However, it was a huge morale boost to the South, and led to many questioning the leadership of Lincoln, and the replacement of many failing commanders in the Union Army.
2) To cut off the Union from the World: This strategy failed in many ways. The cotton & tobacco production that was the heavy-lifting industry of the south failed to gain a large influence with foreign nations, leading to their detriment. They also did not have as large of a navy, and could not put in place naval blockades nearly as effective as the North.
3) Stall: With the first strategy failing, the South took up the strategy of stalling. This allowed them to try to find foreign support, and to draw out the war long enough for the Union to call for a truce. This generally involved fighting skirmishes and running, tiring the Union armies and then striking a heavy blow in a decisive battle.
4) Nativity: The South also believed that fighting in their home front would be easier. This is why most campaigns you see is in the south. Until the commanders understood that it was detrimental to the South's war machine, most fighting took place in the Confederate's home frontier, where they understood the terrain, it was easier to form troops, and supply lines were shorter. Very little was fought on the Northern front, which would prove detrimental in the later years.
5) Foreign Recognition: If the South was recognized as a legitimate government by foreign countries, they can legitimately ask for foreign help. However, no country was exactly interested in doing so, and so the South failed in this sector.
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