It is rather interesting to try and locate Civil War service records. Not that it is necessarily hard to do, it's just that depending on who your Civil War ancestor is, you will have to look in different places.
If your ancestor fought for the North and came from a norther state, then you will have to go to the National Archives for the records. That is because those records were never microfilmed and exist in paper form only. Of course, you don't have to physically GO to NARA...you can order them online from the NARA website.
It's a different story if you ancestor fought for the South, or fought for the North but came from a southern state, or was a member of the US Colored Troops. It is different because those records were microfilmed and now have been digitized. That means that you don't have to go the the National Archives to see the images. You can order the microfilm from the Family History Library, or you can travel to any number of other libraries to view them (such at the Tampa Library). You can also now view them online at Fold3 (what used to be Footnote.com).
And most recently you can find them online at the FamilySearch.org website. The indexes are there for searching and to see the images you are shunted over to Fold3. At first it looks like you have to have a subscription to Fold3 to see the images, but if you put your search name in the appropriate box, you can view the digitized contents of the service record for free. This is made possible though an affiliation between the two sites.
Don't forget that to learn more about ordering records from the National Archives, or to learn more about military records in general and where to find them, check out the list of classes offered by the Pinellas Genealogy Society. Go to the PGS calendar page at http://www.flpgs.org/classes.aspx
If the class is not in the list for the next few months, check back when the calendar is extended.