Going up, approaching the left-hand hairpin: Be to the extreme outside of your lane. Go around the corner staying to the outside, away from the center line. This is not a corner to use the "classic racing line". By being to the outside, you give as much room as possible in case there is errant traffic coming the other direction. For the second (uphill decreasing radius right), again be to the outside (close to the center line) - this gives you better visibility and you will see oncoming traffic sooner and they can see you sooner. Stay to the outside entering the first part of the corner then cut to the inside around the tight (decreasing radius) part when you can see through the corner, this puts you further away from opposing traffic and allows you to keep your speed up ... a lot of people fall down right here simply because they are not carrying enough momentum to get up the hill, which steepens quickly as you turn; being in the wrong gear won't help; being on a screwed-up line through the corner won't help. In either case be prepared to go all the way down to 1st gear and feather the clutch if needed.
Going down, more or less the same thing. Take the left well towards the outside (right-hand car track), not a "racing line", in case of errant traffic coming the other way. As you approach the hairpin you can take a glance over the edge to see if there is oncoming traffic. Stay to the left, near the center line. Normally one would take the tightest part of a corner closest to the inside edge, but in this case, the pavement is so steep there that you don't really want to be doing that. Middle of the lane around the tightest part of the corner is a reasonable compromise. The good thing about this is that you are going so slowly that even if there is other traffic in the corner and someone screws up, it isn't going to be a high-speed crash.
The Appleby Line hairpin at Rattlesnake Point is a lot gnarlier and with poorer visibility.
