Five Finger Filet is based on the European rules of the Knife Game by following certain patterns (in Rounds 1-4) of stabbing the knife in between fingers, for example, 1-2-1-3-1-4-1-5-1-6, etc. (1 being the spot by your thumb, and 6 the spot past your pinky). The primary goal is to not stab your hand while following the pattern.
Round 1 starts off pretty easy, and it progresses to a much harder pattern and faster pace in Round 4. Rounds 1-4 are all based off of patterns though which can be memorized with some practice. My suggestion would be to watch the dot, and never the knife, and work on memorizing the patterns. The best guide I have seen is on Xbox360Achievements, and it works for all versions.
The problem round, is round 5. Round 5 is completely random, and on top of that is very fast. The linked guide has a tip for a possible way to beat it, but I haven't been that lucky.