Hi Casper,
The goal is to beat your opponent either by "sudden death" (National Moral goes below a threshold) or through Victory Points (if the first does not happen). You collect both of them by capturing key objectives (big cities or important stronghold), winning battles, destroying ennemy units, capturing opponent capital,...
In the grand campaign scenario, you start in April or July 1861 and you can play until end of 1865 (except if "sudden death" happens). You have shorter scenarios.
You can freely decide your strategy, but obviously you have some historical (bad Union leaders at beginning, weak southern economy, ...) and physical (difficult to sustain a huge force in Missouri or New Mexico...) constraints.
Maybe you could have a look at some of the
AAR to get an idea of the game.