This depended on the time and the place and the progress of the war itself. Many slaves were freed by the union army well before the war ended or freed themselves and escaped to Union army outposts where what were known as contraband camps emerged for former slaves to live in refugee type situations. Also, from nearly the very beginning of the conflict, well before slaves were formally incorporated into the Union army you would find escaped slaves following the army and assisting it in service positions (e.g. digging trenches, hauling things, cooking, foraging).

As far as at the end of the war, some individual slaveholders would announce the end of slavery to their slaves and would try and get them to stay on the plantation in a wage labor situation. Other times, if people were still being held in bondage after the formal end of the war, union forces would show up and proclaim freedom (this is the origin of the African-American freedom holiday Juneteenth, which marks the entry of the Union army into Galveston, Texas on June 19,1865 and the proclamation of freedom in that city, which was regarded as the last place practicing slavery.

Many enslaved people had no desire to stay on the plantation and wanted to try and find loved ones who had been sold away or taken far away by migrating slaveholders and so they hit the road, looking for their loved ones. Other people just wanted to explore the wider world, an opportunity that they were denied during the years of slavery. Contemporary observers noted a throng of black people on the byways and highways of the south after the war and the lack of willingness to continue old working arrangements and the subsequent fear of economic collapse led to the widespread imposition of coerced work contracts that replicated many of the conditions of slavery in some parts of the South. Tension, of course, was high, as many former slaves believed they were entitled to compensation and a distribution of wealth for their former enslaved labor and resented having no land and property of their own. Revenge killings did happen, but they weren't that widespread and its worth noting that this was a two way street, especially in areas of mixed confederate and union sympathies where tensions from the civil war were settled by private violence after it ended.