ATTACK CHECKS
When attacking someone, you use your Attack Bonus (Weapon Skill + AGI for melee or PER for fire-arms). A basic attack roll is:

COMBAT AND ROUND BASICS
When events and circumstance comes down to the neccessity of detail, the game gets split up into Rounds. Most of the time, this only happens in Combat situations or similar confrontations where movement and timing become more integral-however there ay be other circumstances or times in the adventure where Rounds are used ot break up time.

Rounds are made of 3 actions: Quick Action (Drawing a weapon, the actual calling of a Persona),Move Action (Moving up to 10 Ft. [For Human characters]), and Standard Action (Attacks, Casting Spells, using Skills.)

Present here is a basic overview of a Combat Turn. One gridspace is equivelant to 5 Feet.

Mitsuru and Junpei have responded to a call in downtown Shuujikuto regarding a disorderly, drunken Jack Frost. Mitsuru first attempts to persuade the Jack Frost ti go peacefully, so they can put him in lock-down for the night. Because the Jack Frost is so wasted, the GM sets the Task Difficulty at his Willpower x 2 (In this case, the Frost's Willpower is 15, so the TD is 30.)_
Because Mitsuru is attempting to coerce the Jack Frost, thw GM decides that the skill check will be Influence + Willpower. Mitsuru rolls d20, rolling a 9. Combined with her Influence of 6 and her Willpower of 5, the result is only 19. Since this does not meet or exceed the TD if 30, she fails to get the Jack Frost's cooperation. He becomes a little violent!

Everyone Rolls d20 + Initiative to see who goes when in the round. Mitsuru rolls a 13. Factoring in her Initiative bonus of 8, her Initiative becomes 21. The Jackfrost rolls next highest wth 12, and at a total Initiative of 13, still beats Junpei, who, despite having a better Initiative bonus of 6, couldn't react fast enough with his Init roll of 3.

Round order has been determined, and Mitsuru is acting first. She knows the Jack Frost has an affinity for Ice, and that her Persona Artemesia's magic attacks are all ice-based, so she won't have much luck with spells. She decides to go in with her fleuret for a quick strike.
She uses her Quick Action to draw her sword
She uses her move action to move 5 feet closer
and her Standard Action is an attack on the Jack Frost
Her Attack check roll is a 17. Added to her Attack Bonus with her Elegant Fleuret of 10, the total is 27. The Jack Frost's Reflex roll was a 7, and with hsi Reflex of 18 was just shy of dodging her sword with a total of 25. Mitsuru's sword hits! She rolls for her damage, rolling d20 for a 10, and adding the Weapon Damage of 9 for her sword (3xSTR), bringing her total damage dealt to 19 Damage!

The Jack Frost is angry, but disoriented. His movement consists of stumbling around, and then he casts Bufula on poor Junpei!
The Jack Frost rolls hsi Magic Attack, totaling 55, against Junpei's Magic Defense roll of 53. Poor Junpei is hit by the spell and takes 24 Damage!

Because Junpei's Persona Trismegistus has the Passive ability "Spring of Life", Junpei heals 20 HP at the start of his turn in the round!
Next, Junpei decides to get even. He uses his movement to move over next to the fountain, and for his standard action, he heats things up by casting Agidyne! (A quick action of summoning his Persona to do so.)
Junpei makes his Magic Attack roll, getting a 12! The Jack Frost has also rolled 12, but his lower Magic Defense means he gets struck by the spell. Junpei rolls for Damage, which for Agidyne is 3d20. His results are 8, 15, and 19, for a total of 42.
However! Since Jack Frost is Weak to Fire attacks, the Damage is doubled to 84, AND Junpei gets to roll a Chance to knock the Jack Frost down! He rolls his Luck and gets 1 72, not within his Luck. Junpei fails to knock the Jack Frost down.