This section doesn't concentrate on abilities learned innately (check the character pages for that), but on those which must be found throughout the game. You can find this info both in the character pages and the walkthroughs, but I thought it'd be nice to condense it. After that, we deal with the tiny issue of combo techniques.
Found Techniques (By Character)
Besides for Steena's "HydraShadow", these are all Level 7 techniques.
Doc's "HangTen": In the Tower of Geddon, pick up the Medical Book in the room past the subway turnstiles. Make sure Doc's not in your party, then go to Another Guldove and give him the book. When you re-enlist him in your party, you can equip HangTen on him. This is a high-level HP recovery technique which hits the whole party.
Draggy's "BigBreath": Take him to Another Fossil Valley and bring him to the large skull above the ladder. This is a giant fire attack against all enemies.
Fargo's "Invincible": If you did the "real" way of beating the Black Dragon (via Nikki's concert), Fargo will learn this right after the concert scene. See Part 3 of the walkthrough for more info. This is a single attack.
Funguy's "Myconoids": After getting Serge back, take him back to Home Shadow Forest, in the cave under the waterfall where you found him. Talk to the mushroom (it doesn't matter what you answer it) to learn this. It's a single attack.
Greco's "GraveDigger": Take Greco to his house in Home Termina and talk to the woman there. This is a single attack.
Grobyc's "StrongArm": Take Grobyc to the chest in Chronopolis on the second floor. Single attack.
Irenes' "SirenSong": If you did the "real" way of beating the Black Dragon, take her to Home Marbule once Serge re-enters your party. Go into the first hut you see and talk to the witch doctor twice. It's an all-enemy attack.
Janice's "What'sUpDoc": Take Janice to the Bend of Time and talk to the land octopus. This is a single attack.
Karsh's "Axiomatic": Take him to Another Isle of the Damned and beat Solt and Peppor. It's a single attack.
Kid's "HotShot": Use the Chrono Cross or Mastermune to enter Kid's dream (after Chronopolis). Go up to Lucca's machine on the first screen and press L1, Triangle, R1, Triangle. This is an all-enemy attack.
Korcha's "BigCatch": Once you get Serge back, go to Another Termina. Go up to the covered cage on the screen to the right of the main square and talk to it, then leave the screen, come back, and talk to the owner of the cage. Go down to the shrines, go around to where Korcha's boat used to be, and talk to the mermaid. This is a single attack which hooks one of Sprigg's morphs to attack the enemy, but sometimes misses.
Leena's "MaidenFaith": Leena asks you three questions: two at Opassa Beach, and one in Another Arni. The correct answers to the three questions are "I remember", then "We'll never forget this day!", and (on the dock) "I'm Serge!". You need at least 2 out of 3 correct to get this technique. When you get Serge back in your party, go to Home Arni with Leena in tow and talk to her grandmother to get it. It raises Leena's attack power and her accuracy goes up to 99% temporarily. Supposedly she gets auto-revived if she dies, but in my experience that hasn't worked.
Luccia's "TestAmeba": When Serge gets back in your party, take Luccia to the top left corner of the kitchen (bottom floor, second door from the left) and go down the sewers. Hold right and follow the upper path to find a blob; examine it to get this technique, which is a single attack.
Mojo's "HoodooGuroo": After getting Serge back, talk to the fisherman in Home Arni, then take Mojo back to the fisherman's house in Another Arni. Go downstairs and talk to Laserey, Aurey, and Lickey, in that order. (That's the bottom left, top right, and top left cat.) This is a single attack.
NeoFio's "BamBamBam": Take NeoFio to Another Sky Dragon Isle. Talk to the land octopus, then leave the screen and come back. Push the land octopus and keep hitting the Action button to get this technique, which is a single attack.
Nikki's "LimeLight": Take Nikki to the S.S. Zelbess in Home World. Go up the crow's nest to the left and talk to the sailor to go to the Magical Dreamers ship. Talk to this world's Nikki to learn the technique, which is an all-enemy attack.
Norris's "TopShot": Take Norris to Another Viper Manor and enter the parlour (second from left, top floor). Talk to this world's Norris to get it, which is a single attack.
Orcha's "DinnerGuest": Take Orcha to Home Arni and enter the pub. Go behind the counter and talk to the chef, Belcha, to get this single attack.
Orlha's "SisterHoods": Take Orlha to Home Guldove and talk to Doc in the first house. It's a single attack.
Pierre's "SlapOfCyrus": In the Tower of Geddon, pick up the Prop Sword in the large room where you fight the Tragediennes. Then, once you've gotten Serge back, make sure Pierre's not in your party and talk to him in Zappa's house in Another Termina. SlapOfCyrus is a single attack which will always miss unless Pierre has all three Hero's items equipped (Medal, Shield, Blade).
Poshul's "Unleashed": Take Poshul to Home Arni and talk to Leena at the docks to get this single attack.
Razzly's "Raz-Flower": Razzly must NOT have been in your party during the Hydra Humour quest, and she must have been in your party during the Ice Breath quest. After beating Chronopolis, take her to Home Water Dragon Isle; the tree in the center should be in flower now. This technique raises magic power for all allies.
Riddel's "SnakeFangs": You get this at the same time as the Mastermune; see the Walkthrough Part 3 for more info. This has a certain chance of restoring all of Riddel's Element usage.
Skelly's "OnARoll": Take Skelly to Home Termina. Enter the bar and talk to the bar lady to get this single attack.
Starky's "StarStruck": Take Starky back to his ship in El Nido Triangle in Another World after actually entering Terra Tower. It's an all-enemy attack.
Steena's "HydraShadow": Go to Another Hydra Marshes. Go left till you reach the blue platform where you fought the Wingapede before, and jump in the hole. Defeat the De-Hydrate to get this Level 5 technique, which hits all enemies.
Steena's "GaraiShadow": Take Steena to Home Isle of the Damned and return to where you fought Garai. Examine the gravestone to get this all-enemy attack.
Turnip's "VegOut": Take both Turnip and NeoFio to Another Viper Manor. Go to the balcony at the top floor and examine the pool to get this single attack.
Viper's "FlagBearer": Take Viper to the bar at Home Termina and talk to the bar lady. Go into the small room at the left and enter the secret room at the left side (face upwards). Look at the flag on the wall to get this technique, which raises all of Viper's stats for a short while.
Zoah's "Toss&Spike": Take Zoah to his room in Another Viper Manor (second from the right in the first floor) and open the chest to get this single attack.
There are very few combination attacks in the game. To do a combination attack, both (or all three) characters must have the required Element Level, as well as at least one Stamina point, plus none of the techs can have been used yet. After the attack, both techniques which make up the attack will be exhausted. One last thing: Combos may be a completely different Element than either technique which makes it up.