While the South believed that Lincoln would act to end slavery once he took office in 1861, he had repeatedly tried to reassure the South that he would not do so. However, Confederate states began succeeding in December of 1860, before Lincoln had even taken office. Even after succession, Lincoln again committed himself to protecting slavery where it existed, and he proposed the 13th Amendment to the Constitution to protect slavery in the states where it was practiced (the Amendment failed, and the 13th Amendment would become the act that freed the slaves in 1865).

After the Confederate states succeeded, Lincoln did not recognize them as distinct from the Union, as he saw succession as illegal. He also tried to avoid taking a course of violence, and he wanted to pursue peaceful negotiation. However, when Confederate forces attacked Fort Sumter in April 1861, which was a federal property in Charleston harbor, the Civil War broke out. 

Lincoln took many steps to avoid war.  He said publicly that his goal was not to end slavery.  Lincoln hoped that the Lower South would come back to the Union on their own––after all, this was not the first time that South Carolina had talked about secession.  In Lincoln's First Inaugural Address, Lincoln hoped that the South would listen to the "better angels" and return to the Union as he referred to secession as "nothing but anarchy."  He said this in the hopes that the South would listen to a reasonable argument and return.  

Militarily, Lincoln put the responsibility of secession on the South by not reinforcing Ft. Sumter.  He sent in a round of supplies which was actually approved of by outgoing President Buchanan, but when the ship was fired upon, he did not send in more supplies.  Even when the fort was fired upon, Lincoln refused to send the commanding officer Major Anderson assistance.  While this cost Lincoln valuable political points within his own party, he wanted it to appear that the South was the aggressor in this war so that it did not appear to the outside world that the South was being oppressed.  

I would say that Lincoln's basic strategy for avoiding war was trying not to antagonize the South.  He did this through his actions and through his words.

In his inaugural address, Lincoln was very conciliatory.  He spoke about how there was no need for bloodshed and he talked about how the North and the South were one country with a common heritage.  He also pledged that he would not try to "interfere" with slavery in the places where it was legal at that time.

In terms of his actions, Lincoln was also pretty conciliatory.  For example, he did not send reinforcements to Fort Sumter.  He thought that that would be too aggressive of an action.  Instead, he just tried to send supplies.

So the point is that Lincoln tried to do and say things that would A) keep the Union together and B) avoid making the South too angry.  These were the steps he took to try to avoid war.