The genealogy website Fold3 is offering all its Civil War era records for free through April 15, 2017.
Along with Civil War military records the 1860 census is also free. You can access the Civil War Pension index to see if any of your ancestors applied for a pension for their service in the war. Most valuable in my opinion is the Civil War "Widow's" pension index. These records include the actual documents. A wealth of information can be found in the Widow's pension files. These records are rather expensive to order from the government (around $75 for the full document). This gives you a chance to download these files for free if you are fortunate enough to find one for your ancestor.