First Bull Run was a chaotic, amateurish affair fought by two armies that were untrained and unprepared for war. Meanwhile, civilians from Washington (including Senators and Congressmen) rode out to picnic and watch the grand victory of the Union over the Confederacy. The Union commander -- Irving McDowell -- actually had a good battle plan and almost beat the Confederates under Pierre Gustav Toutant Beauregard. However, the timely arrival of Confederate reinforcements (sent by train, a first in war!) turned the tide and lead to an ignominious rout of the Union forces. Union soldiers fled the battlefield, swamping the pleasure watchers, and ran nearly back to Washington. Confederate forces, exhausted and disorganized from the battle, did not follow the routed Union forces. It goes without saying that this was not how Lincoln wanted the war to begin. Causalities from the battle were light in comparison to what came later -- the North lost approximately 2,900 men (460 killed, 1,100 wounded, 1,300 captured or missing) and the South lost about 2,000 men (387 killed, 1,600 wounded). Compare that with the Battle of Antietem in September 1862 when almost 3,600 men were killed alone.
Beside being the first major land battle of the war, Bull Run is notable for several reasons. First, it (and the subsequent Battle of Shiloh in April 1862) shattered forever the belief that the would be over quickly and cheaply. Second, it revealed severe deficiencies in both armies. Lincoln dismissed McDowell and replaced him with George B. McClellan, a general who had already won a string of minor victories in Western Virginia. McClellan replaced incompetent commanders, reorganized the forces, and trained them. Ultimately McClellan failed on the battlefield, but his tenure as commander left the Union with an army -- the Army of the Potomac -- which defeated the best the South had.
One of the great things about the sesquicentennial is that several sites are running blogs that follow the war's progress. The New York Times, in particular, is following it on their "Disunion" blog, which so far has had some great posts. I would recommend reading today's, to get a fuller description of Bull Run.
