Coyori

Normals
5B - Not a low hit, doesn't cancel to specials, but is fast and chains to 2B. Also gives a small amount of frame advantage, where 2A and 2B are at disadvantage.
2B - Staple low poke. Good range, easy to hit confirm out of, but is at disadvantage on block.
6B - Two hit Overhead. Very, very good. Slight disadvantage on block but can't be punished except with Gatchi. Becomes essential in Heat Up mode.

5D - Excellent poke. Can be hit confirmed into 623D on hit.
2D - Large sliding sweep, but at big disadvantage on block. Spaced correctly though, it can be unpunishable. Good for getting knockdowns.

j.D - Three hit jumping attack. Very good crossup, good for starting combos. Excellent overall.

Air Dash - Coyori can dash in the air by hitting 66. You can cancel the air dash into an attack very quickly. You can also instant air dash using this.
Chains
5A -> 5A, 2A, 5B, 2B
2A -> 5A, 2A, 5B, 2B
5B -> 2B, 6B
5C -> 5D

2C(1) -> 2B

j.A -> j.B, j.C, j.D
Specials
236A/C - Tea Is Ready ➀
A short forward poke with her tray. Fast and is the entry point to her Rekka chains.
C version is slower but has more range. (More damage?)
┕▶ A
(From ➀)
- First Tea ➁
A quick rush hit. Low damage, but very fast.
┕▶ 6A
(From ➁)
- Second Tea
A rapid 3-hit attack. Safe on block, good for chip or building bar, or to finish a combo after First Tea. However, there is a gap between First Tea and Second Tea so it is possible to Gatchi if predicted correctly.
┕▶ 6B
(From ➀)
- Lukewarm Tea
Coyori's 6B. Works exactly as if done as a normal and thus can be canceled to j.C in Heat Up.
┕▶ B
(From ➀ or ➁)
- Dart Attack ➂
A crossup attack. Very slow, easy to hit her out of, but can be useful on occasion to be confusing or bait a Gatchi.
Hold B to perform a fake version. It will still crossup, but not attack. Also very slow.
┕▶ C
(From ➀ or ➁ or ➂)
- Gratuity Please
A very slow overhead. Has fairly short range as well. Can be comboed off of on hit however, so may be useful on a rare occasion.
┕▶ D
(From ➀ or ➁ or ➂)
- Bitter Tea
A low sweep. Knocks down on hit. Unsafe on block so use with caution.

623B/D - Cat Windmill
Upper-cut like attack, but has no invincibility at all. Very fast startup.
D version is excellent for punishing attacks from far away, and to use to end combos.
B version can be used in a few juggles, or possibly as anti-air. But not very useful otherwise.
┕▶ 2D
(From 623D Only)
- Duster Attack
Overhead smack off 623D. Knocks down and gets some extra damage. Use this any time you use 623D.
If 623D wiffs or is blocked, this can hit some characters who are standing. But it won't make it safe.

Supers

236236P - Crazy Cat Dance
Forward rush super. Covers distance very fast, and can punish things from full screen. No invincibility however, and will generally not hit airborne enemies correctly.
236236K - Cat Storm
Mash all buttons and the joystick for extra hits.
Vertical attack super, hits a lot but doesn't do a lot of damage even at maximum mash. Not invincible, although it has very short startup so it might be useful as AA in some situations.
Heat Up
Muuteki Mode!
During Heat Up, Coyori is significantly powered up. Her movement abilities are enhanced, her combo abilities are GREATLY enhanced, as are her mixups, her specials and supers. Heat Up is Coyori's biggest strength and is absolutely critical to playing her well.

Enhanced Movement

During Heat Up, Coyori gains the ability to Double Jump. After double jumping, Coyori can always air dash, even if one was already used! So it is possible to get two jumps and two dashes.
She also gains the ability to Jump Cancel all of her air normals, but only on hit and not on guard (and only once per jump obviously). By extension, she can also Instant Air Dash Cancel (IADC) her air normals, which is a very important tool for combos.
You can shortcut an IADC by doing 9, neutral, 6, very rapidly. So for her basic j.B loop, you would do:
Jump, j.B, 9, neutral, 6, j.B |> Repeat

In addition, the following ground moves gain the ability to be jump canceled on hit while in Heat Up:
2D, Gratuity Please, Bitter Tea

Finally, her j.A gains the ability to be canceled directly into an air dash on hit or block, up to 7+ times in a single jump! Jump canceling will also reset this, so it seems possible to keep it up for a very long time if timed properly.
The usefulness of this, however, is pretty questionable.

Enhanced Normals

Most of Coyori's normals are enhanced in some way during Heat Up. Almost all of them are faster (especially 5A) or can hit more times. These are especially of note:

6B - First hit can be canceled into j.C. Extremely important mixup tool for Coyori! See Heat Up Combos section for more details.
2C - Hits 3 times instead of 2.
2D - Hits twice. Second hit can be jump canceled into air juggles on hit.

Enhanced Chains

Probably the most important part of Heat Up are the improved Chains Coyori can do. During Heat Up, she gains the following chains:

5A -> 5C, 2C, 5D, 2D
2A -> 5C, 2C, 5D, 2D

5B -> 5C, 2C, 5D, 2D
2B -> 5A, 2A, 5B, 5C, 2C, 5D, 2D
6B -> j.C

5C -> 6B, 2D
2C -> 2D

Enhanced Specials

┕▶ C
(From ➀ or ➁ or ➂)
- Gratuity Please
Can be jump canceled on hit.
┕▶ D
(From ➀ or ➁ or ➂)
- Bitter Tea
Can be jump canceled on hit.
j.623B/D - Cat Windmill
Cat Windmill can be done in the air during Heat Up.
236236P - Crazy Cat Dance
Wall slams, and can be juggled off of.
236236K - Cat Storm
Mashing can get significantly more hits in. But damage isn't really enhanced by that much.

Instant Heat Up Mixups

Coyori can make extra good use of Instant Heat Up techniques by using them to start a mixup directly. Examples are:
6B+A+C j.C |> ...
(Overhead)
2B+A+C 5C 5D ...
(Low)
2D+A+C jc.B IADC j.B |> ...
(Long Low Poke)

See the Heat Up Combos section for all the details on these combos.

Heat Up Resets

While you can finish most Heat Up combos with 623D, it's actually much more worth your meter to reset with them. Take the following combo for example:
2B 5C 5D 236C, D, (j.B IADC j.B |>)*3, 5A

The 5A forces a reset and gives you plenty of time to setup. From here, you can do a few things, but most obviously, you can mixup into 6B or 2B, and again get a full combo on hit.

Combos

Basics

2A 2B 236A, A, 6A
Easy, fairly safe and easy to hit confirm with. Builds decent meter on block.
Air Dash, j.A j.B |> 5B 2B ...

5B 2B 623D 2D
5B 2B 236236P

5C 5D 623D 2D
5C 5D 236236P

5D, 623D 2D
Staple long range poke into DP. Very useful to hit confirm with.

Gatchi Counter

(0 Far)
5D 623D 2D
[?]
(0 Close)
5C 5D 623D 2D
[831]
(1 Close)
5C 5D 236236P
[1193]
(1 Either)
Heat Up (5C) 5D 236C, D, (j.B IADC j.B |>)*3, 623D
[1309]

High Gatchi Drive

(0 Any)
j.D(1) |> 5C(1), 623B, 623D 2D
[631]
(1 Any)
j.D(1) |> 5C(1), 623B, 623D(1) 236236K
[1011]
Same story as with the LGD combo. 623D must hit them as low to the ground as possible.
(0 Mid)
6 5C(1), 6 5D 623B, 623D 2D
[778]
(1 Mid)
6 5C(1), 6 5D 623B, 623D(1) 236236K
[1135]
Advanced combo, only works at mid screen and easy to mess up, but gives much better damage.

Low Gatchi Drive

(0 Any)
66 66, 5B 5C 5D 623B, 623D 2D
[804]
(1 Any)
66 66, 5B 5C 5D 623B, 623D(1) 236236K
[1132]
To cancel to the super, you need to have them low to the ground when 623D hits. Timing is different depending on the character.

Heat Up

6B(1) j.C(1) |> 5B 2B 5C 5D 236C, D, (j.B IADC j.B |>)*3, 623D or 5A
Always works on standing, but will miss short characters who are crouching. Always works on Deathbringer, Donvalve and Watson
At the end of the combo, you can either finish with a DP or reset and go for another mixup. Very recommended if you have some Heat Up time remaining.
6B(1) j.C (wiff!) |> 5B 2B 5C 5D 236C, D, (j.B IADC j.B |>)*3, 623D or 5A
On short characters, you must use this version instead. You will wiff the j.C entirely, but then link into a 5B when hitting the ground. Timing is strict, but this is one combo you really need!
2B 5C 5D 236C, D, (j.B IADC j.B |>)*3, 623D or 5A
2D, (j.B IADC j.B)*3, 623D or 5A