If you know what regiment and company your Civil War ancestor was in, then you’ll find a wealth of information searching on that. Usually you can find out the names or roster of people in a company (usually about 100 men). From my great-great grandfather’s pension record, I knew he was in Company G, 93rd Indiana Volunteer Infantry.
When you search for the regiment, try variations like “93 Indiana Infantry” and “ninty third Indiana Volunteers.” Sometimes you find sources such as an old book on the regiment that has been placed online. Most of these can be searched by name inside the book.
Some information is available through the state archives, so go to those sites once you know what state your ancestor’s regiment was from. The regimental histories give a list of the places, some dates and the battles the regiment was in. This lets you see where your ancestor was during different times of the war.
I found it helpful to map out the movements of the regiment so I could visualize it better. This is my web page Tracking the 93rd Indiana Infantry‘s locations during the Civil War.