Your 1876 10 pfennig coin from the old German Empire catalogs for about $20 US dollars in almost uncirculated condition. The coin in my picture is in average circulated condition, so the catalog value goes down to about $10. Fully uncirculated 10 pfennigs catalog at $20 or more. The dates before 1889 catalog above $50 when in uncirculated condition. Please check the meaning of 'catalog' using our Important Terminology link at the upper left.
Remember: Do not clean your coin. Cleaning ruins value.
Look for an H mint mark on your coin. If it is there, the value goes up substantially.
Just about all of these 10 pfennig coins from the German Empire catalog in the $2 to $5 region for worn coins. There are exceptions. The series runs from 1873 to 1916. In 1889 the design of the reverse changes a little and in 1915 the composition changes from copper-nickel to iron and zinc (see this link for information on the iron and zinc coins.
Below are the better dates for the copper-nickel coins, worth about $10 to $20 catalog value for coins in worn condition (more if in well-preserved condition). See if you have any of these:
1873 all mint marks
1873H worth 100s of US dollars
1909F, G, J
Finally, if you can find an 1892J you have hit the jackpot. Catalog values start at $5000!