Officially the Civil War began at 4:30 A.M. April 12, 1861, when according to Mary Chestnut's diary, the St. Michael's bells chimed. As the wife of a Confederate Officer, Mrs. Chestnut was well aware of the ultimatum given by the then seceded South Carolina that the Union army abandon Fort Sumpter, South Carolina as they were now the enemy. However, there are two additional answers to this question that are quite considerable, especially to those who study the Civil War, myself being one of them. The first was in 1859, abolitionist John Brown orchestrated a raid on a federal magazine (weapon arsenal) in the hope of initiating a slave uprising. Unfortunately, John Brown's plan backfired, the slaves never stood up and revolted and shortly after Brown was executed for treason. Due to his bravery however flawed, John Brown is considered the 'meteor' of the war. Even Frederick Douglas claimed that he lived for the slave's emancipation, John Brown died for it. The second was after Lincoln's victory in November 1860. South Carolina stated publicly that if Lincoln won the election it would leave the Union. That December, South Carolina seceded from the Union, forming the Confederate States of America...willing to war against the United States of America.
To my way of thinking, the American Civil War started on April 12, 1861. This was when the Confederate forces in Charleston, South Carolina attacked the Union garrison that held Fort Sumter. Fort Sumter was on an island in the Charleston harbor. This was the first actual military action of the war.
I suppose you could argue that the war began when the Southern states seceded following Lincoln's election, but I do not think that would be all that accurate. If Lincoln had let them go, the war would never have happened. So I would definitely go with the firing on Fort Sumter as the start of the war.
The first armed conflict between the two opposing sides to the American civil war, which can be considered the actual start of the war, was the attack on the Union Military post of Fort Sumter in South Carolina. On April 12, 1861 the Confederate forces fired on the fort and forced it to surrender. However the formal declaration of the war by the Confederates can be considered to be when when they they regarded the call by Lincoln, on April 15, 1861, for Union troops to regain the fort, as a declaration of war.