This is actually a very good effort.
1. Columns are states, gray for the Confederacy and blue for Union.
2. The time scale runs vertically, from 1861 at the bottom to May 1865 at the top.
3. Movements of major field units are marked by black lines, solid for Union and dashed for Confederate. Lines are further highlighted by color — gold for Union, green for Confederate.
4. Engagements are marked by circles, according to the size of the battle. Most are numbered to a key (presumably lost), but the larger and more important ones are labeled directly. Circles within the larger battles are colored green (Confederate) or gold (Union) to indicate the winner.
5. Sieges are indicated by solid red bars
In this closeup, you can see the siege and capture of Atlanta, the march through Georgia and capture of Savannah at the end of 1864, Sherman's move north into the Carolinas with Johnston keeping ahead of him, Hood's army's diversion into Tennessee toward Franklin (oddly labeled as a Confederate victory) and Nashville, after which it fades away to nothing, and (far right) the ongoing stalemate at Petersburg until a final and sudden collapse in April 1865. There's a lot going on in those colored lines and circles.
Finally, this diagram owes a lot to
Charles Minard's famous diagram of Napoleon's disastrous Russian campaign of 1812. This CW diagram is harder to follow, but it compresses much more information that Minard's.
Bringing the