The Northern Strategy to win the war was designed by Gen. Winfield Scott, and was known as the "Anaconda Plan." This called for a blockade of the Gulf and Atlantic Coasts and also the capture of the Cumberland, Mississippi and Tennessee Rivers. This would not only cut the Confederate States in two, it would also economically strangle them as would the constricture of an Anaconda, hence the name. The Southern strategy was not as well defined; but largely consisted of "cotton diplomacy," hopes of gaining recognition and support from the European nations which bought Southern cotton. It was to this end that Gen. Lee twice invaded the North, in hopes of gaining recognition. This strategy was apparently known and appreciated by the Union, as it was after Lee's invasion of Maryland and the Battle of Antietam that Lincoln issued the Emancipation Proclamation, which placed European nations in the moral dilemma of supporting slavery (which they opposed) if they supported the South.
The North's strategy in this war was relatively straightforward. It knew it had to conquer the entire South and set up a plan accordingly. The basic plan was to blockade the South from the sea and then to invade along various strategically important routes to cut up the Confederacy.
A major problem for the South was its lack of a true overall strategy. Some in the South wanted to fight a defensive war. They realized they did not have to defeat the North and that all they had to do was hold out long enough to make the North give up the fight. But others wanted to be more aggressive. This made for a rather uncoordinated approach to the war. One other aspect of the South's strategy was an attempt to use their economic power (their status as major cotton supplier to Europe) to get European countries to take their side (at least diplomatically) in the war.