Another important piece of information to know is which state your ancestor served with. Knowing the soldier's full name and the state he served from will be a big help in narrowing down your search. If you have a Genealogy Room or History Room in your local library, spend some time there going through books relating to the War in the State that your ancestor was from. Look for books which might contain information on the particular Company or Regiment you ancestor served in. Instead of taking a lot of time searching through a whole book, go to the Index and try to locate anything that might be a connection to the individual or the Company he served in.
Many local libraries have listings or files of individuals buried in cemeteries.
These may lead you to the gravesite of your ancestor. If you know what branch of service your ancestor was in, this can also help to narrow down your search. There are many Company and Regimental histories listed on the internet also. Go to your Search Engine and type in the name of a particular Company or Regiment that you might be interested in. Those States that have the staff and equipment will usually go into a deeper search at fifteen cents or more a page for duplicated records.