Feint "Drift"
Technically speaking, it is not possible to actually drift in Initial D Arcade Stage. However you can follow the feint motion to achieve higher exit speeds and more fluent turning.
The feint was introduced in version 1 and fully utilized by Akina Master Extra HC. The basic concept is still out-in-out except that before aproaching the turn from the outside and staying out the whole time, you start on the inside.
Figure a1:
1) Approach the turn from the inside lane
2) Swing the car to the outside
3) Turn the car inside.
To follow these steps, one should know the timing of turn back outside, roughly 50-100m depending on the turn. It is important to keep everything else constant meaning normal out-in-out braking at the same time you normally would without feint. This is the biggest problem for people first starting to use this technique, they forget to slow down. If you don't have full understanding and control of out-in-out line, it is not recommended that you try feint yet.
Another advantage of following the feint line is that it effectively prevents understeer. Sometimes if the wheels on the machine are not good, they'll shake while your car appears to be going straight, this might cause sudden movements before a corner causing the car to not turn at all for the corner. Feinting keeps most of the car's movements in your control so that understeer will not occur.

5 In 4 Out
Introduced in version 2, 5 in 4 out was initially a hard concept to understand. The name, however, is quite self explanitory. One approaches a corner and does all the braking and slowing down in a higher gear (on 5 gear cars: 5th gear). Then during the acceleration part of the corner, one would shift down to a gear (in 5 gear cars: 4th gear). The idea behind this is that 5th gear keeps a higher speed but the car still slows down enough to complete a turn. The player shifts down a gear for faster acceleration.
Sounds like a simple idea but if one is used to 4-in-4-out shifting during a turn, they will notice that you must brake a lot more for 5-in-4-out.

Magic Eraser
Initially dubbed "The Outrun Technique" eraser is now an essential technique in IDv3. Introduced early version 3, eraser was intended for the game Outrun 2 only.
In version 3, one would shift up a gear then down a gear again which causes the car to turn a little more. HOWEVER! Do not expect ID to behave like outrun, the outrun eraser is performed during a turn while for it to be effective in Initial D, eraser must be performed as earliest as possible before a corner. If you have already learned feint, feint a little earlier and turn in a little, then eraser and complete the turn as usual. With eraser, it is possible to complete some turns full gas when you normally wouldn't be able to. Some turns can be exited with higher exit speed by using multiple erasers but anything more than 3 is not recommended. Most turns are just 1 eraser and a few are 2. There are rare situations when 3 is needed. Remember that eraser works by helping your car turn a little more, so angle the car towards the corner first, (just turn the wheel a little inwards) then shift up and back down quickly. This technique will not make your car go faster as in Wangan Midnight: Maximum Tune (dubbed the Gacha Technique).

TST
TST is an English acronym for the Chinese word: Tsat Sheung Tsat literally translating into erase-up-erase.
Introduced a few months after eraser, TST is quite literally bullshiit.
On turns where the player has enough room + distance to prepare for the turn, they can use the TST technique.
The first form of TST, I will use the first turn of Akina as an example. About 200m from the corner, the car should be as close to the inside as possible but leaving enough room for the car to turn inwards a little (usually near the middle of the lane). There should be room left because at this point, the player needs to use the Eraser Technique twice.
The car will be locked going that direction (right for the first turn of akina). Then turn the wheel the otherway (left) as fast as possible, then swing back and erase again and brake, apex, etc.
As you can see, this is quite unbelievable, it is not even driving anymore.
However this with this technique, exit speeds can be 1-2km faster. It is not recommended to use this technique untill you are very familiar with the game concept (usually at most 2 seconds away from world record time). The concept of TST is basically a mega feint and multiple eraser combined, by erasing twice early, the car naturally wants to turn that way, swinging out just gives more time to get the correct line and eraser back in once more.