I've taken it upon myself to write a guide of sorts to those who need it / don't understand how to play yet.
Buttons
There are six face buttons in total. Since I assume you're using a keyboard, I'll use the keyboard buttons instead of the gamepad buttons.
Z - Light Melee Attack
X - Heavy Melee Attack
C (Z+X) - Special Button 1
A - Light Danmaku Attack
S - Heavy Danmaku Attack
D - Special Button 2
The special buttons have four different functions to them. Your special moves, Spell Cards, and Last Words are all activated using the corresponding special button + any direction, and you may customize which specials / spell cards are activated by pressing whichever direction + whichever button you may want, and you may do so for each individual character. It's sort of like Super Smash Bros., except you have two buttons for a total of 8 specials instead of one button.
C/D+Up
C/D+Down
C/D+Left
C/D+Right
Mechanics
The bar at the bottom of your screen is your stamina. You require stamina in order to use special moves. Blocking (I think) gradually decreases your maximum stamina.
In order to use a Spell Card, the blue portion of your health bar must be completely covering the white portion, then you have to press the Special Button + Direction of the spell card you want. Entering the button combination once 'declares' that you are using the spell card. The background will get all fancy and you'll be glowing slightly. Using the combination again performs the spell card. Spell Cards (on the character customization screen) has a shinier outline than normal cards, so whichever combination you set the shiny cards to, those will be the combination required to use Spell Cards.
There is a favor percentage below your health. It can go up to 100% and down to -100%. Favor is what wins you the game if you fail to deplete your opponents health. Once you have 100% Favor, you will be able to use your Last Word. Last Word cards (on the character customization screen) has a red outline, so whichever button combination you set your red card to, that will be the combination required to use Last Word.
With the Last Word, there is no need to 'declare' the attack. It will automatically use the Last Word the first time you enter the combination, so be careful not to get confused.
Character-Specifics
Each character has their own passive ability. There are different ways to use these passive abilities depending on which character you are using. Since there are only three characters for now, I will go over the ones I know.
Marisa - She has the ability to augment every fourth spell she uses into a more powerful version of that spell. Every time you use a spell, one star (out of three) at corner of your stamina bar fills up. When you have three stars, the next spell you use is more powerful, and the stars return to emptiness.
Ichirin - She has the ability to enter a rage mode of sorts. When you take damage (or take hits in general, I think blocking works too), the Japanese symbol at the corner of your stamina bar grows larger and redder. When it gets large and red enough, it starts to flame, and Ichirin and her cloud will turn red. During this mode, (I believe) your attacks are stronger (at least it feels like they are).
Reimu - I have no idea what her orbs do right now. Needs confirmation. She can, however, jump from one side of the screen to the other by double tapping towards the edge of the screen.
Menu
I will now explain the Profile menu.
In order, the list is (according to what they do, not what they are actually named):
Customize Characters
Button Configuration
Profile Icon
Create Profile
Copy Profile
Delete Profile
Rename Profile
Extra
By pressing the F buttons while in a match, different effects occur:
F1 - Instantly gives your player 100% Favor and your opponent -100%
F2 - Same as above, but swapped for Player 2.
F3 - No clue as of yet (something about guarding, from very weird testing)
F4 - Turns on Practice Mode, In which your Health recovers after being hit and your stamina recovers faster than normal. It also gives you a full special bar.
F5 - Sets the maximum health during practice mode.
F6 - Sets the maximum stamina during practice mode.