There are lots of ways to "fail." The right way to "fail" depends on your meaning.
Animated: "fail"
The general sign for failure (as in the opposite of success) slides the dominant V (or K) hand (palm up) slides across the top of the non-dominant flat hand palm from the butt of the hand to past the fingertips.
FAIL (in general)
Note: The graphics are in the right order. The first graphic shows the dominant hand starting its movement from above and behind the non-dominant hand. Then it slides across the palm of the non-dominant hand and off into the air a couple inches.
FAIL as in "get an F on your paper."
Sample sentence: Have you ever gotten an F in class before?
FAIL as in "lose a competition":
Animation:
Notes: