Before the EP:
Before the slaves would have been freed with a legal argument. Prior to the war, slaves were property of their owners. The Northern states were obligated legally to return the escaped slaves under the Fugitive Slave Act.
Union General Benjamin Butler was stationed in Norfolk, VA. 3 slaves that were leased to the CSA army for construction of defensive batteries at Sewell's Point escaped to the Union lines. A CSA officer approached the Union line and demanded Butler return the slaves under the Fugitive Slave Act.
Butlers response was the Fugitive Slave Act did not apply in this instance, because the CSA had succeeded from the USA and the laws that bind it, and therefor could not use the laws meant bond US citizens together. Further, with slaves considered property, and under the international laws of war, any property that aids the enemies war effort can be seized as contraband.
Butler stated that as a foreign power, he was under no obligation to return the three slaves to a CSA officer, and would hold them as contraband.
This argument was moved up the chain of military command, and eventually to Congress. Congress would reaffirm this decision with the Classification Act of 1861 and the Act Prohibiting the Return of Slaves.
Leading up to the EP, and after the EP, freeman were a huge problem for the Union Armies. Slaves would have known that escape to Union lines meant freedom, but the CSA had forces to stop the escapes. What would happen is a Union force would enter an area and slaves would follow the army. Hence, the Union troops provided the security.
This was a major problem for cavalry. Cavalry would detach themselves from the main columns and supply lines. When away from the supply lines raiding, the on foot freeman would slow the on horse soldiers down. The slaves could not have known that the cavalry could not support them, but all the same it was a problem.
When the slaves were able to get to the main body of the army, supply systems would have been established to support the influx freeman. The Union would offer to pay the freeman to join the Union, which many did. Others would have been used by the Union armies for labor.
The below comes from Chapter XXX from Grant's Memoirs
It was at this point, probably, where the first idea of a "Freedman's Bureau" took its origin. Orders of the government prohibited the expulsion of the negroes from the protection of the army, when they came in voluntarily. Humanity forbade allowing them to starve. With such an army of them, of all ages and both sexes, as had congregated about Grand Junction, amounting to many thousands, it was impossible to advance. There was no special authority for feeding them unless they were employed as teamsters, cooks and pioneers with the army; but only able-bodied young men were suitable for such work. This labor would support but a very limited percentage of them. The plantations were all deserted; the cotton and corn were ripe: men, women and children above ten years of age could be employed in saving these crops. To do this work with contrabands, or to have it done, organization under a competent chief was necessary. On inquiring for such a man Chaplain Eaton, now and for many years the very able United States Commissioner of Education, was suggested. He proved as efficient in that field as he has since done in his present one. I gave him all the assistants and guards he called for. We together fixed the prices to be paid for the negro labor, whether rendered to the government or to individuals. The cotton was to be picked from abandoned plantations, the laborers to receive the stipulated price (my recollection is twelve and a half cents per pound for picking and ginning) from the quartermaster, he shipping the cotton north to be sold for the benefit of the government. Citizens remaining on their plantations were allowed the privilege of having their crops saved by freedmen on the same terms.
At once the freedmen became self-sustaining. The money was not paid to them directly, but was expended judiciously and for their benefit. They gave me no trouble afterwards.
Later the freedmen were engaged in cutting wood along the Mississippi River to supply the large number of steamers on that stream. A good price was paid for chopping wood used for the supply of government steamers (steamers chartered and which the government had to supply with fuel). Those supplying their own fuel paid a much higher price. In this way a fund was created not only sufficient to feed and clothe all, old and young, male and female, but to build them comfortable cabins, hospitals for the sick, and to supply them with many comforts they had never known before.
So the EP really did not change what was already happening on the ground. The EP was more for the rest of the world. Slaves were being freed and protected by the Union army, and able bodied freeman were used to help the war effort.
edit: English and added the next paragraph to the quote