Quick Jump

Dash & Dash Attack
Press the control pad twice in the same direction for a dash (extra burst of speed). Press the B-button afterward to cause the character to attack.
Light Attack & Combo
Press the B-button to attack (light attack). Press the B-button three times in a row to complete a combo attack. Press the B-button four times in a row and the combo attack will end with a heavy attack.
Heavy Attack
Press the control pad in the direction of the character you are attacking and then the B-button.
Upper Attack
Press the control pad in the opposite direction of the character you are attacking and then the B-button.
Chase & Attack
After you have sent a character flying away from you, press the control pad in that direction immediately to follow the character (chase). If you manage to successfully chase the character, time the right moment to press the B-button to attack the character. The added damage depends on how squarely you hit the character, if at all.
Jump & Air Attack
Press the A-button to jump. If you press the A-button in the middle of a jump, the character perform an "air action" that varies from character to character. If you press the B-button in the middle of a jump, the character will attack (air attack).
Defend, HP Recovery, & Ichikoro Gauge
Press the L-button to create a quick shield to protect your character from attacks for a moment. Hold the L-button to recover lost HP and fill the Ichikoro Gauge (allows for one-hit KOs). You can be attacked while attempting to recover lost HP or filling the Ichikoro Gauge.
Special Attacks
There are three types of special attacks: Power, Shot, and Trap/Set. You will use those types to set the Ground, Air, and Defend Special Attacks at the beginning of each fight as well as after being KOed in the middle of a fight (if you are KOed). Press the R-button to peform the Ground Special Attack. Press the A-button to jump and then the R-button in the middle of the jump to perform the Air Special Attack. The Defend Special Attack means that you are invulnerable to that particular type of Special Attack. These attacks can cause one-hit KOs if the Ichikoro Gauge is filled for your character and the character that you are attacking is not defending that particular kind of Special Attack.

The Gizoid was found by Sonic, who "linked" to it and named it "Emerl" due to its connection to the chaos emeralds. In theory, Emerl is the most powerful character in the game. Based on how much you replay the game and/or fight characters, Emerl will learn the moves of all the other characters in the game. Once a move has been learned, you can set Emerl to use that particular move. So, Emerl's usefulness is going to be a result of which moves Emerl manages to learn. There are also special ultimate and combo moves that can be unlocked or acquired in certain parts of the game that also help make Emerl tough to handle.
Sonic is one of the fastest characters in the game, and has average attacks and defense. His healing and ichikoro gauge charging abilities are on the weak side, but his quickness makes him easy to use in a fight.
Tails has decent healing & ichikoro gauge charging abilities, average speed, can fly, above average defense, and has gadgets that help him out in a fight.
Only E-102 and Chaos are slower than Knuckles in this game. His attacks, defense, and healing abilities are decent, but his ichikoro gauge charging ability is one of the best. Timing is very important if using Knuckles and his special attacks will help immensely if you have trouble using him.
Shadow is the fastest character in the game and many of his attacks are powerful and his defense is decent. He has some of the worst healing and ichikoro gauge charging abilities. He is easy to use in a fight due to his quickness.
Rouge has average speed and attacks. She has the ability to hover in the air, which might prove useful for attacking from above. Her defense, healing, and ichikoro charging abilities are not very good.
Emerl's "Mom" and the new promoter of boxercising, Amy, is pretty quick and has decent attacks. Her healing is pretty good, too.
Cream is average in speed and mainly weak in attacks. Her healing and her ichikoro charging are some of the best in the game causing her special attacks to become your best friend when using her.
E-102 Gamma
One of the slowest characters in the game, you can only play as E-102 outside of Story Mode after fighting against E-102 in Sonic's episode. Its attacks are usually powerful and its healing is one of the best. Whenever it is KOed, it explodes, which will cause a lot of damage to any opponent(s) within range--unless it is the KO that ends the battle in which case no one is harmed. The damage can be minimized by immediately pressing the control pad in the opposite direction that the character is blown toward (if the opponent isn't KOed by the explosion).
The slowest character in the game is Chaos. You can only play as Chaos outside of Story Mode after fighting against Chaos in Emerl's episode. Its attacks range from weak to powerful though is healing is one of the better ones. Its attacks do tend to have wide ranges and some have "hidden" effects that are beneficial.
Eggman is not a playable character in this game. He is just attempting to take over the world for the zillionth time and is responsible for finding the Gizoid (named "Emerl" by Sonic).
E-121 Phi
These robots were created by Eggman as a replacement for Emerl since Eggman couldn't get Emerl to work as intended at first. These robots look exactly like Emerl, but are gray-colored, and will have all the abilities of either Sonic, Tails, Knuckles, Shadow, Rouge, Amy, Cream, or E-102 when you face them. They are powered by chaos emerald shards.
Guard Robo
These robots look exactly like E-102 and have all the same moves as E-102, but are gray-colored. Unlike E-102, these robots will not say anything to signify that they have been KOed and are about to explode. So, you must pay attention to their movement. These robots were created by Eggman, who has also sold them to people that use them as guards.

As you play the game, in any battle that has Emerl as a participant, there will be an ability that the other characters (Sonic, Tails, etc.) have that Emerl will learn. You can set Emerl to use any move that he has learned in the Edit Screen--press the R-button while on the field or whenever the story allows/requires to access it. You do need to watch the skill points you have as well as the amount of skill points a move requires. You can only set Emerl to use a skill if you have enough skill points. You earn 10 skill points for each chaos emerald Emerl receives. You earn anywhere from 1-6 skill points for each fight that you win in which Emerl is a participant. Each card has a star rating (1-6). For each star, the card requires 5 skill points for it. So each card will require anywhere from 5-30 skill points to be used. Only the default skills have a zero star rating and therefore do not require any stars, but the default settings are extremely pathetic.

In Emerl's episode, at Tails' Lab, you can take part in Virtual Training. If you choose to enter, you must defeat three random opponents (virtual copies of Sonic, Tails, Knuckles, Shadow, Rouge, Amy, Cream, E-102, Chaos, & Emerl) without ever being KOed once. In the first round, you must KO each opponent once; in the second round, you must KO each opponent twice; in the third round, you must KO each opponent three times; etc. You have to get through at least five rounds to earn a capture card.