Start with going to your library. Look for "Uniforms of the US Army" by H. A. Ogden and the many other illustrated books concerning uniforms and 19th century fashion (yes fashion!). Dover publicatons reprints many.
Your state may have a military museum or similar archive that you can visit and and look for similiar items. If you are from MA there is a museum on Salisbury St. in Worcester and I believe most towns have a Historical Society that may help. You may even find old photos of people wearing the dress you have.
Take photos if you can and get photos of details like buttons and cuff ornaments. Look inside the clothing for makers/tailors tags (some will show street address) a good way to date things.
James B. Ronan II
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