Each of Will's three forms have different attack patterns, and they can be taken advantage of in different ways. Let's start with the moves that all of them share (each character starts with these moves and doesn't have to go to a specific Dark Space to get them).
Pressing the A button (or whatever button you set to attack on the Start Game screen) will unleash a regular attack on unsuspecting enemies. Will attacks with his flute, Freedan with a sword, and Shadow with a tentacle (?). Will's attack is the weakest, but he jumps forward slightly when he does it, which means he has an extra split second of invulnerability; just keep attacking and most weak to medium enemies are fish bait. Freedan's is the fastest and has the longest range; Shadow's is the strongest and is almost as fast and far-reaching as Freedan (and he seems to have a bit more sideways range).
Tap forward twice to go at a run. If you change direction or press Attack, your momentum will die and you'll stop running. Running is necessary for navigating slopes (you frequently must run down one slope and continue running to be able to go up the next one).
Hold L or R to execute the Telekinesis move. This has a twofold use: 1) Blocks certain projectile attacks; very useful if you have good timing. 2) Draws things towards you. It works on Dark Gems (those little red/gray things enemies drop), the bouncers in Mu, and a few different types of statues.
Will has this attack from the beginning. Hit attack, then quickly tap forward. This causes Will to do a regular attack, then a jump attack. The jump attack does about 1.5 times as much damage as the regular attack, plus while Will's jumping he can't be hurt. This is excellent against some of the more stolid enemies in the game.
Found in: Itory Village
To execute this move, hold the Attack button down. Will will begin flashing green. He'll slowly flash green twice, then he'll begin flashing quickly. When this happens, his power is full. Release the button to do a dash move. This move has much longer reach than his sword and does about twice the amount of damage, but in close quarters you'll never be able to charge it up without being hit. Also, you can't dash past a wall, whereas your flute can frequently hit enemies on the other side of a wall. The Psycho Dash can knock holes in certain walls, as well.
Found in: Mu
Tap forward twice to make Will run, then hit attack. This slide can not only hit for decent damage (which can be further augmented after you get 20 Red Jewels), it's also useful for sliding through small gaps. Will can usually hit twice or three times with one Psycho Slide, plus it can be used quickly. The only (rather large) downside is that Will's vulnerable for a second as he gets up; if you didn't defeat the enemy you slid into, chances are you'll get walloped before you can get away.
Found in: China's Great Wall
Hold down the Attack button like you would do a Psycho Dash, but instead of letting go, press L then R alternately until Will begins to spin. You'll then see four arrows surround him. If you let the arrows go away, Will can move around for a short time, damaging enemies at no risk to himself (but it goes away very fast! Watch it!). If, instead, you press a direction while the arrows are displayed, Will will rocket off in that direction. This is used to cross small ramps in the later parts of the game.
Found in: Diamond Mine
Hold down the Attack button; Freedan will glow red slowly twice, then rapidly. When he glows rapidly, his power is at full (like Will's Psycho Dash). Releasing the button will shoot a ball of fire across the screen. Although the Dark Friar doesn't do all that much more damage, its long range is very useful (and sometimes necessary to defeat enemies on the other side of gaps or walls). Plus, if you get over 30 Red Jewels, or get the Dark Potion in Euro, the Dark Friar will gain in power such that when it hits enemies (or when you press the Attack button again while it's in flight) it will split into four very large fireballs which whirl off the screen, doing very heavy damage. Excellent!
Found in: Mountain Temple
Like the Dark Friar, build up Freedan's power by holding down the Attack button. When it's full, press R or L. Two blue shields will surround him and circle around him for a short time. They'll hurt enemies they touch. Not a necessary skill, but it comes in handy.
Found in: Ankor Wat
This one's simple to pull off and can be useful: Just hit the Attack button when you drop off a cliff or ledge. Freedan will shake the ground when he lands, and all enemies will be immobilized for a little while.
Found in: Pyramid
Shadow must have the Aura equipped to use this skill (you get it at the same time you get Shadow). Pressing the B button will cause Shadow to melt. He can't be hurt in this form, but he can't move or do anything either. He'll reform in a few seconds. The real point of it, though, is that if he's standing over an extended floor in the Pyramid (you can see the bricks below the floor go down for a bit) he can drop through the floor and land on the floor below.
Found in: Tower of Babel
This can only be used in the very last battle; just press the Attack button to send a phoenix out to attack. This is very similar to the use of the Phoenix in Soul Blazer, the prequel to Illusion of Gaia.