What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There were a few major varieties of the 1876 S Trade Silver Dollar. The difference between the varieties has to do with a combination between the obverse design type and reverse design type.
The Type 1 obverse is the earlier design used on the front of the Trade Dollar from 1873 through 1876. The Type 2 obverse is a newer design used starting in 1876 and all later years. It is fairly easy to distinguish the difference between the two varieties. The Type 1 design features only three fingers on Liberty's extended hand holding a branch - whereas the Type 2 design features four fingers on the hand. Another feature to look at is the scroll or banner bearing the word "LIBERTY". The bottom ends of the scroll points towards the left on the Type 1 design - whereas the ends of the scroll hangs downwards on the Type 2 design. The difference between the Type 1 Obverse vs Type 2 Obverse is depicted above in the example comparison image.
The Type 1 reverse was the earlier design used on Trade Dollars minted from 1873 through 1874 and some of them from 1875 through 1876. This design features an extra berry on a branch under the eagle claw on the right side of the portrait. In addition: The bottom-most arrowhead tip ends just above the "0" in the words/numbers "420 GRAINS".
The Type 2 Reverse is a newer design used on some Trade dollars in 1875-1876 and on all Trade dollars starting in 1877 and onwards. This design is missing the berry under the eagle claw and the bottom-most arrowhead tip ends just above the "2" in "420". These features are depicted below. The difference between the 1875 Type 1 Reverse vs Type 1 Reveres Trade Dollar is depicted below in the example comparison image: