The fishtail is somewhat inappropriately named, because it more resembles the skeleton of a fish than its tail. I often put two fishtail braids in my fiance's long hair and one in my little cousin's tresses. I use more than the four sections described by lakeonfire.
Instead, I start with two major sections but rather than dividing them each into two more, I take a small strand from the far side of one and add it across to the other, than repeat with the other side and so forth until I reach the bottom.
The result of this is that the fishtail takes longer to create but ends up looking more decked out and even more fish-bone like.
Viewers of the finished product often have no idea what it actually is but comment on how it looks like an especially intricate braid. Others who are familiar with the names and existence of such haircrafts will recognize it immediately and give props.