To determine the value of an 1886 silver dollar, identify the coin by the design and the mint mark. Look up the coin on a coin value website, such as CoinStudy.com or CoinValues.com, as of 2015. Keep in mind that coin value varies significantly depending on the condition of the coin, and just because a coin has a certain value doesn't mean that it's going to sell for that amount.
An 1886 silver dollar is a Morgan silver dollar. The mint mark for these silver dollars is on the back of the coin towards the bottom, directly above the word "Dollar." An "S" indicates that the coin was minted in San Francisco. An "O" indicates the coin was minted in New Orleans. If the coin doesn't have a mint mark, it was minted in Philadelphia, as that mint location didn't use a mint mark.
For the 1886 Morgan silver dollar, coins minted in San Francisco tend to be worth the most at good, fine and extremely fine quality levels. However, the most valuable are uncirculated 1886 Morgan silver dollars. An uncirculated coin must have no signs that it was in circulation. Once a coin is in circulation, it loses its mint luster, and its high points accumulate wear.
Most 1886 Morgan silver dollars are worth about $10 to $30. The value for uncirculated coins is much higher, and a uncirculated 1886 Morgan silver dollar from New Orleans can be worth upward of $1,000.