At the beginning of the Civil War, the main Union strategy was the "Anaconda Plan" of Gen. Winfield Scott. This was a term given to it by its opponents, who thought it was too slow and tentative.
Scott's plan was to squeeze the South slowly, without having to really mount a major invasion of the South. The first objective of this strategy was to blockade the South's ports. This would prevent the South from obtaining supplies from foreign countries. The second objective was to control the Mississippi River. This would prevent the South from moving supplies around within itself.
In the end, this was a major part of the North's strategy that won the war. However, an invasion was eventually necessary. In this invasion, the primary objective of the North was to cut the South in half multiple times, thus preventing areas of the CSA from helping one another.