Naturally, Yosuke is a very fast character who can both run all over the stage and shower the enemy with fast attacks. Just don't let the opponent go on the offensive, and you'll be fine.

Normal moves
5A/2A - Your regular small palm/foot strike. S-Rush (the 5A mash combo) knocks up the enemy, so you can follow it up with an air combo or Garudyne.
Close 5B - Yosuke makes an upward spinning cut with a kunai.
Far 5B - Yosuke makes an upward cross cut with his kunais. Similar to BlazBlue Hazama's 5C.
5C - Jiraya quickly kicks upwards. You can make an additional boomerang cut by pressing 5C again.
5D - Jiraya rushes forward with a palm thrust after a short pause. Since he is left wide open for retaliation, you should use this move to close the distance and avoid losing your Persona too soon.
jA/jB - Kunai slashes that have almost no differences between each other. Their direction is slightly different, and that's it.
jC - Jiraya performs a wind barrier attack diagonally downwards. Mostly used on ground-bound targets as a jump-in.
jD - Simply the aerial version of 5D.
Throw (C+D) - Yosuke dashes back and forth and cuts the enemy with his kunai, poisoning them.

Special moves
"Evacuate" (B+D) - Yosuke performs a powerful counterstrike if he is hit. Though it's not as good as Chie's Hyper Counter, it's still good.
Tentarafoo (236C/D) - Jiraya places a star-shaped seal on the ground wherever he is at the moment. If he hits the enemy with it, he blows some dust on them, and they become confused (their directional inputs switch places). This move is unblockable and has good reach, but its cooldown is a bit long. Use the Confusion status in pressure, so the enemy has to deal with a cross-up-like situation when the status ends.
Dash (236A/B) - Yosuke dashes towards the enemy and stomps on them, using them as a jump pad and becoming airborne. This is a risky move, but allows for easy cancels into aerial moves.
Leaping Dagger (j236C/D / j214C/D) - Yosuke throws some daggers downwards, with the C version throwing the daggers diagonally downwards and D version throwing them right below Yosuke. If the daggers hit the enemy, you can connect them to Moonsault or Garudyne.
Moonsault > Crescent Moonsault (j236A/B / j214A/B > A/B) - Yosuke makes a quick jump (forward for A version, backward for B version). You can make up to three follow-up attacks with Crescent Moonsaults, that make Yosuke jump around even more. You can easily use it in combos, including comboing this into Garudyne.
Transform Ripper (j2C/D) - Jiraya teleports Yosuke to the ground, as Yosuke himself makes a quick slash. Basically counters any anti-air moves that your opponent may throw at you.

Super Move
Garudyne ((j)236236C/D) - Jiraya envelops Yosuke in a green tornado, which rapidly spins around the screen. You can control the direction by pressing the appropriate directional buttons. It has some invisibility frames, so feel free to use it as a reversal move, but keep in mind that the enemy can easily block it.

Awakening Super
Sukukaja (214214C/D) - Raises Yosuke's speed greatly. Moreover, his ground dash becomes an attack by itself! There are very few ways to counter this, so use it as often as possible!