Chrono Trigger/Techniques

Crono
Element: Lightning Cyclone is a useful tech for taking out groups of enemies early in the game, although it's even better when combined with some of the double techs you'll have. Life is particularly handy since Crono is a fixture in your party, and just keep in mind what your best physical attack or magic spell currently is. Luminaire is the most powerful Single tech in the game under normal circumstances.

Lucca
Element: Fire You'll mostly just want to use the best fire spell Lucca has available.

Marle
Element: Water Marle uses water magic in the form of ice. As you can see she's almost entirely support spells. Haste is an extremely useful tech against long, drawn-out bosses like the Black Tyrano. and Life 2 is the best revival method in the game. Her drawback is the lack of healing spells that affect the whole party, but she does get a lot of Double Techs that compensate for that.

Frog
Element: Water Frog is required for the whole sequence in Magus's castle, and he has a good physical attack otherwise. The Heal spell is very useful, and Frog Squash is a killer, doing extreme amounts of damage when HP is low, for example after using a Revive... keep this in mind.

Robo
Element: Shadow Robo is very slow, so he needs a lot of Speed uppers before he can unleash his full potential. He learns a damage-all tech early, which is useful during the Factory section where he must be in the party. Heal Beam is also useful.

Robo cannot learn magic, but can deal shadow damage.

Ayla
Element: None In general you'll probably be best off using the most powerful physical tech she has, and charm can be very useful for getting rare items. Dino Tail functions much like Frog Squash.

Ayla uses entirely physical attacks since she predates the existence of magic on the planet.

Magus
Element: Shadow Magus has every kind of magic available to him and a strong physical attack, although his specialty is shadow. What's not to love? One interesting note about Magus is that his versions of Lightning 2, Fire 2, and Ice 2 are about 30% more powerful than those cast by Crono, Lucca, or Marle, which makes him effectively the best Water magic user in the game among other things.

Double Techs
Every set of two characters, excluding Magus, has three double techs between them.

Triple Techs
One rule of thumb is that every three character set which includes Crono and doesn't include Magus has a triple tech. Thus, Crono Marle Frog have one, Crono Marle Lucca, etc. In addition to these triple techs however, there are some hidden ones that can only be activated by finding a hidden "rock" accessory somewhere in the game and equipping it on one of the characters involved in the triple tech. To use any of the special triple techs you'll need to wait until Chapter 24 when you're finally able to choose your party without Crono.

Tech Required
These triple techs require the characters to have the requird abilities and fight together for one battle.

Accessory Required
These triple techs require one of the characters who are able to perform the triple tech to wear an accessory unlocking the ability.