I'm going to recite from memory how the game flow proceeds, this isn't a direct translation of the tutorial, so the wording is going to follow mostly my own, as opposed to my near-religious zeal of staying true to the original Japanese descriptions when I drew up the card spoiler list.
1: Each player rolls a die; the player with the higher rolled die value gets to determine whether to go 1st or 2nd.
2: Each player receives 3 white Force points and draws 6 cards from his deck. If you go 1st in Turn 1, go to step 4.
3: You receive 1 white Force point; for each character in your playfield, you receive 1 Force point of each character's Force alignment.
4: Draw 1 card.
**** You may perform step 5, 6, 7, and 8 in any order ****
5: You may discard any number of cards from your hand. For each card discarded in this manner, you receive 1 Force point of each discarded card's Force alignment.
6: Play Character, Action, and/or Counter cards by spending the play cost shown on the card. Obey the Force alignment shown in the play cost. White Force points may be spent to satisfy only white pips in the play cost; any combination of blue, green, red, and yellow Force points may be spent to satisfy white pips in the play cost. If a character has a Triangle special ability, you may spend the activation cost to trigger said ability or decline payment. Characters played into your playfield normally will enter play in a frozen state.
7: You may spend the activation cost on a character with a Square special ability to use to trigger said ability. After a character uses its special ability, it enters a frozen state.
(NOTE: Characters with Circle special abilities are continuous effects --- payment of their Force costs are outside of your control. If preconditions in the Circle special ability are met, the game will check your Force point balance to see if you are able to satisfy the Force cost; if you cannot, then effects of said ability do not occur.)
8: You may Support/Backup any number of characters in your playfield with character cards in your hand, where Support/Backup refers to the effect of replenishing 1 character's current HP, if it is below the printed HP value, with the printed HP value of 1 character card in your hand. To perform a Support/Backup, donor and recipient must have matching Force alignments, and you must pay 1 Force point with corresponding Force alignment.
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9: You may declare any number of characters in an attack. BP is the attack power and HP is the defense power of each character. When a character's HP is reduced to 0, it leaves play and enters the discard pile. There are 2 types of attacks that you may perform: Normal attack and Fusion attack. A normal attack is one in which each character enters an attack, alone. A Fusion attack is one in which 2 characters join forces in an attack and requires the payment of 8 white Force points; only 2 characters with matching Force alignments may do so. Once all the attacking characters have been decided, press the button of attack declaration to announce your attack(s).
10: Opponent may declare any number of characters to defend against an attack. Once all the defending characters have been decided, press the button of defense declaration to announce your defense(s). Opponent may also play Counter cards during his defense declaration.
If a character is assigned to defend against a Fusion attack, and if the combined BP of the Fusion attack exceeds the HP of the character defending against that attack, the damage difference --- Penetration damage --- is dealt to the defending player. (which I referred to as spill over damage; later I will go back to revise the wording to more closely mirror the original Japanese description)
11: Declare end of turn. If you have more than 8 cards in your hand, you must discard your hand down to 8 cards. You receive 1 Force point of each discarded card's Force alignment.
12: Turn goes to opponent. Go to step 3.
Hope that helped