If you are not familiar with how to research Civil War regiments, I suggest that you find a copy of Tracing Your Civil War Ancestor by Bertram Hawthorne Groene, ISBN:0-345-36192-X. This book is readable and includes much useful information. The National Archive's Civil War Records Tutorial includes a thorough explanation of the kinds of information in their collections. These sources will give you an idea of what information is available and what types of clues to look for.
At a minimum there are several pieces of information that you need to begin your search: a name, unit number, place of residence, dates, and date/place of death. You need not have all of these. But the more information you have the easier you search will be. Each of these items can help you locate clues to your ancestor's service.
National Archives and Records Administration
The National Archives (a.k.a. N.A.R.A.) will have the most information on any given Maryland Union Unit: muster rolls, company order books, military and pension files, record of movement cards, and more. They also have Confederate material as well. The types of records mentioned above are located at Archives 1 (on The Mall in Washington, D.C.) Civil War photographs are located at Archives 2 (College Park, Maryland.) See the web page for more info.
Maryland Historical Society
201 W. Monument Street
Baltimore, Maryland 21201
The society houses a museum and an extensive library of Maryland history. Museum highlights include: a Civil War room, furniture, silver, and more. The libraries collection's include extensive manuscript holdings, a historical structures index, clipping files, and more. Maintained seperately is a major collection of historical images, from all periods of Maryland history.
Maryland Hall of Records
350 Rowe Boulevard
Annapolis, MD 21401
The official repository for Maryland State Records, the Hall of Records features a large (decently lighted) reading room, library of key reference books pertaining to Maryland, microfilm readers, and very helpful staff.
If you reach this point, and you still haven't found more then passing mentions of your unit, and you wish to continue, your last great hope is the unexplored country:
Maryland newspapers from 1861 through the 1920s+. After looking through eight (!) scrap books filled with clippings on the 2nd Maryland Infantry alone, it became crystal clear that there is a mass of Maryland unit info that has not been utilized. The Baltimore Sun, and other Maryland newspapers of the time are filled with everything from first hand battle accounts, casualty reports, memorial dedications, reunion announcements, etc. The problem is the looking through 60 years or so of newspapers on microfilm for that choice bit of info.