The first resource that you ought to use--and the resource I found I remembered most of the facts from when writing the exam--is the DVD box set of the Public Broadcasting System's The Civil War - A Film by Ken Burns. This is probably the most comprehensive documentary on the Civil War made to date, and tells the story of the war largely through the primary documents from that era such as speeches, letters, and so on. Any American university or public library worth its salt should have these DVDs available for borrowing, and if they don't, you should ask them why. Watching the entire DVD set once should give you a firm foundation for writing the exam; watching it three times is even better.
For some extra video material besides the Ken Burns DVDs, there are free video lectures from Yale University on the subject of Civil War and Reconstruction available. Also, Annenberg Media offers some relevant videos in its series, A Biography of America, located at Learner.org. Videos 9 - 12 are all relevant to the study of the Civil War. Despite being shorter than the Ken Burns DVDs, they still have some additional useful content, and you'll know more going into the exam after watching these videos and the Ken Burns ones than if you watch the Ken Burns series by itself. To watch these, you'll need to sign up for an account at Learner.org, which is free to do.
I suggest mixing up reading with watching the video materials so that you don't get bored from doing a single form of study all the time. The U.S. Department of Education offers a list of free resources on the Civil War here, and it's worth reading through them during your studies.
You should know about the different battles of the Civil War (memorize which commanders were at each battle for both sides; this is important), and leaders of the Civil War (when you open this link, click on the thumbnails to learn more about each person, and visit Wikipedia to get any additional information on them). There's also a good timeline of the Civil War available from the Library of Congress.
Some specific facts you ought to know are that more troops died of disease in the war than anything else, the total number of troops who died during the Civil War was around 650,000, the bloodiest battle of the war was Antietam, the first battle was at Fort Sumpter, the slave-holding states which remained in the Union instead of joining the Confederacy were Missouri, Kentucky, West Virginia, and Maryland. You'll pick up a lot of these facts by watching the Ken Burns DVDs.
Note that the title of the exam says, "and Reconstruction." You'll need to know about what happened after the war, as well, for which I strongly recommend reviewing the Reconstruction Timeline on George Mason University's website and reading up on each event mentioned in it.
If you study all of these resources, you should have no problem passing the DSST Civil War and Reconstruction exam. Good luck!
RELATED LINKS (Open in new window)
A Biography of America (Annenberg Media)
Leaders of the Civil War (Smithsonian Institution)
List of American Civil War Battles (Wikipedia)
List of Free Civil War Resources (United States Department of Education)