Wow, this should be a bit of an interesting thread.....
I usually start my laps to the outside of the track, the outside being the opposite side of the first turn. As I approach the turn, I hit my braking point and brake in a straight line while shifting down. I immediately begin to cut across the track after letting off the brakes and accelarate to the apex of the corner. I will usually let off the gas and just tap the brakes if I'm carrying too much speed. I then punch the gas (or gradually apply pressure with spin happy cars) and turn hard to make it around the corner without scraping the wall or running off course. For tricky turns (like the turn before the second tunnel at Apricot Hill), I may keep the car in 3rd gear and coast around the turn so I won't have to deal with all the sliding and spinning. If I'm trying to get the fastest lap possible, I'll shift down to the appropriate gear and punch the gas along with countersteering at the same time to keep the car straight.
For computer cars, when I'm ready to make a pass, I'll usually fall in line behind them. Then as we approach the corner, I'll duck to the inside and brake later than usual to get by them. I make sure to hold the inside line so they won't execute a "double pass" on me.
On the straights, the same rule pretty much applies from the part above about entering the first turn. "Slow in, fast out" is the ideal way for me to get around the course. For sweepers (like the one at Apricot Hill or Midfield), I'll start the turn on the outside then cut across the track and get the 2 left wheels on the rumble strips, managing the throttle to maintain stability. And for chicanes (like the ones found at SSR11 or Cote D' Azur), I'll enter the turn from the outside as usual and turn in to point the car in between the inside and outside walls, brake, and accelarate on through the corner, sometimes clipping the inside curb on the exit.
And just so I won't discriminate, I'll even throw in my rally driving techniques.
I enter turns from the outside as usual, but this time I brake while turning in to swing the back end out, all the while shifting down to the appropriate gear. I accelarate full throttle through the turn, making any countersteering adjustments to keep the nose pointed towards the inside fence. Since the dirt causes more friction than the road, I usually lose speed in the drift and shift down to a lower gear to get an extra boost of accelaration coming off the corner. For the extra sharp 180 degree turns, I use the hand brake instead of the regular brakes to send the back end almost all the way around. Shifting down to 1st gear, I fight the slide and hit the throttle to keep the car from sliding too far out to the outside of the track and countersteer greatly to get the car pointed back in the right direction. Looks great on replays
