The National Archives Civil War records have been digitized and are available on Ancestry.com. This week (through Thursday), you can search them for free.
By searching a name, you can learn when your soldier enlisted, which company he served, and what became of him. The company name is often a hyperlink to the unit itself, listing all the battles it fought and linking to a list of all soldiers in that unit. Many of the battles also link to a narrative description of the event.
Learn more about the digitized records here.
And be sure to check out this collection of Civil War portraits.