Light = A
Heavy = B
Controls vary depending on your method of play.

Standing Light - A short jab
Standing Heavy - A far straight
Crouching Light - A far slide
Crouching Heavy - A short uppercut, knocks opponent into the air

Jumping Light - A downforward punch
Jumping Heavy - A downward elbow, crosses up the opponent

Downforward Light - A far dash punch
Downforward Heavy - Shorter 3 dash punches
Downback Light - A jump slam, can cross up
Downback Heavy - A standing smash explosion, huge hitbox, invincible until recovery frames

Super Charge - Builds 1/4 meter
Downforward Super - Combines downforward light and heavy for high range and 3 hits
Downback Super - Combines downback light and heavy for a jump smash explosion, also invincible until recovery frames

Forward Throw - Picks up opponent, makes small explosions around them, and slams them down for a 2 hit total
Backward Throw - Picks up opponent, makes small explosions around them, and tosses them down behind her for a 2 hit total

Specials are performed by holding downforward or downback and holding either A or B.

Super Charge is performed by pressing both A and B at the same time.

Super attacks are performed by holding downforward or downback and holding BOTH A and B at the same time.

Throws are performed by holding either forward or back and pressing B while close to the opponent.

All moves are viewable in the video below.

NOTES:
- = NOT AVAILABLE. MOVE HAS NONE OF THOSE FRAMES.
KD = KNOCKDOWN

TG = TIL GROUNDED

15- OR 16- = 15/16 OR LESS, DEPENDS ON WHEN THE ATTACK IS PRESSED

?(?)?(?)? = ACTIVE(BETWEEN)ACTIVE(BETWEEN)ACTIVE, ONLY THE ACTIVE WILL HIT, SO IF THE FIRST MOVE HIT MISSES, ITLL TAKE (BETWEEN) UNTIL 2ND HIT

ADVANTAGE AND DISADVANTAGE: POSITIVE MEANS SAFE, NEGATIVE MEANS UNSAFE

RECOVERY+KD: UNTIL CHARACTER IS PUT INTO KNOCKDOWN, YOU HAVE THAT MANY FRAMES TO JUGGLE THE OPPONENT

Not all of this could be 100% correct, and if any of it is wrong, I apologize and would like correction. I did this on my own without looking stuff up, so it's entirely possible.

Apparently with this game, to figure out a normal combo, the 1st move's advantage has to be higher than the 2nd move's startup. This is unlike some other fighting games in which advantage can be equal to or higher.
In a similar fashion, for a cancel combo, the 1st move's hit stun has to be higher than the 2nd move's startup.
Not all things will combo even though the frame data suggests it should: distance is a huge factor in this. If you're pushed out of reach for the move to hit, or even for the first active frame(s) to hit, the move will not combo.
An example of this is DF.SU to C.L : according to the frame data, DF.SU's advantage of 8 should combo into C.L's startup of 7, but because DF.SU pushes Naomi back so far, it isn't possible.

-= FEW BASIC COMBOS TO SPARK YOUR IDEAS OFF OF =-

J.L - S.L - S.L - DF.H

J.H - S.L - C.H - DB.SU - C.L

S.L - C.H - DB.SU - C.H - DB.SU - C.H - DB.L (CORNER ONLY)

J.H - DF.SU - DF.L


===========================================================
-= FEW SETUPS (WIP, NOT SURE IF THEY'RE GOOD OR BAD) =-

J.H - S.L - C.H - DB.SU - C.L - DF.L - F.GRAB
J.H - S.L - C.H - DB.SU - C.L - DF.L - J.H - S.L - S.L - DF.SU
J.H - S.L - C.H - DB.SU - C.L - DF.L - J.H - C.H - DB.SU - C.L - DF.L - F.GRAB
J.H - S.L - C.H - DB.SU - C.L - DF.L - J.H - C.H - DB.SU - C.L - DF.L - J.H - C.H - DF.L - J.H

J.L - S.H - F.DASH - F.THROW
J.H - S.L - S.L - DF.SU - F.DASH - S.H - F.DASH - S.H - F.DASH - F.THROW

J.H - S.L - C.H - DF.L - C.L - DF.SU