Chrono Trigger Game Systems
Chrono Trigger has a generally simpler combat system than its Final Fantasy brethren, but despite the simplicity there is still plenty of depth. It really walks a fine line, and does so quite well. However, understanding what lies beneath the surface is still advantageous.
Stats
The stats in Chrono Trigger are fairly straightforward, but there are a few interesting tidbits you should pay attention to. Specifically, that speed does not increase with level, and that power doesn't affect bows or guns. Also note that when any stat (aside from HP and MP, but including level) hits its maximum, it will be displayed as ✩✩. In general this means the stat is 99, except in the case of speed where the maximum is 16.
HP
HP works the same way here as in other RPGs. Chrono Trigger's maximum HP is 999, and every character will reach that plateau by the time they hit level ✩✩ (and generally long before). One interesting note is that dead characters will be restored to 1 HP after battle, meaning that Revive is a battle-only item.
MP
MP is also pretty standard, though it is used not only for magic but for all Techs. MP caps at 99, and as with HP, every character will hit this maximum long before level ✩✩. The most expensive Techs cost as much as 20 MP, which is a significant chunk of your total. Accessories like the Gold Stud can help make your MP go much further.
Power
For most characters, power increases the damage they deal with normal attacks and Physical Techs. However, this is not the case for Lucca or Marle, both of whom use hit to determine damage instead of power. Power can be permanently increased by 1 for a character by using a Power Tab. Several characters will hit ✩✩ power by level ✩✩, but by the time you're anywhere near that level, nothing in the game will be any challenge anyway. Thus, don't hesitate to give Power Tabs to whoever you use primarily as a physical attacker. (Just don't give them to Lucca or Marle!)
Hit
Hit is your physical accuracy stat, and doubles as the physical damage stat for Lucca and Marle. Everyone's Hit is at least halfway decent, and there's no Hit Tab to increase it, so you're usually stuck with what you have. A few accessories can increase Hit (sometimes called Strike in their descriptions).
Magic
Magic is much like power, but for elemental attacks. Don't assume that this is not a useful stat for characters who don't use magic (like Robo), or even that it only affects magic techs beginning with a ✩. Magic influences any tech that deals elemental damage, even non-magic ones like Laser Spin. Even Ayla gets some use from magic, though only during Combo Techs. As with power, some characters can max out their magic stat naturally, but won't do so until extremely high levels. You need to decide whether to use your Magic Tabs to increase your main casters' power, or supplement that of your secondary casters like Crono and Frog.
Speed
Speed is an interesting, and very important, stat. Unlike the others, Speed doesn't increase by level (though Robo gets a permanent bonus during a late sidequest). It also has a very low maximum of 16. Speed directly influences your battle gauge's refill rate, meaning that a character with double the speed of another can take actions twice as often. This is obviously a huge advantage, so Speed Tabs are among the most previous items in the game. I would recommend giving them to your slower characters, because they will gain the most from them. Also, keep in mind that while ✩Haste doubles your speed, the maximum value is 24, so speed scores above 12 are slightly less impressive than they seem.
Evasion
Evasion allows a character to avoid physical attacks, which is certainly nice, but you have little control over it. There are no Evasion Tabs, only a few accessories that supplement this score. Keep evasion (and stamina) in mind when choosing a party to fight enemies with a lot of physical attacks, though.
Stamina
Stamina decreases the damage taken by physical attacks. Like evasion, you have very little control over stamina, but it's still a useful stat to be aware of. Physical attackers tend to have the highest stamina scores.
Magic Defense
Magic defense is basically stamina for elemental attacks (and presumably for resisting status ailments). It is another stat you don't have much control over, but can be very useful against magic-using enemies. Casters have the highest magic defense scores.
Techs
Without a doubt, Chrono Trigger's Tech system is one of its finest features. There are three types of Techs: Single, Dual, and Triple. Single Techs basically take the place of the spells you would find in most RPGs, though they are as often special attacks as actual magic. The Dual and Triple techs are what make Chrono Trigger unique, because they allow multiple characters to work together to create powerful and sometimes unique effects. It is worth knowing how to learn and use these Techs to your best advantage.
Single Techs
Every character can learn eight Single Techs over the course of the game. To learn Techs, you must earn TP from battle. Crono, Lucca, Marle, and Frog can only learn two Techs each at first. To learn their third, they must meet Spekkio at the End of Time. Once they have done this, they can freely learn their remaining five Techs.
Most characters have an elemental affinity, and their elemental techs are all of this element. Magus is the exception to this rule (and many others), as he gets Techs of every element, though his most powerful are Shadow-elemental. Robo also has Techs of several elements, though Ayla has no elemental Single Techs at all. Single Techs are straightforward, and while they're not as exciting as Combo Techs, they will be your staple attacks in most battles.
Dual Techs
The game really gets interesting once you start learning Dual Techs. Every pair of characters (not including Magus) can learn exactly three Dual Techs with one another. To learn a Dual Tech, first each character must know the Techs that make it up. At the end of combat, if both characters are alive, they will learn the Dual Tech (including during the combat in which a required Single Tech is initially learned). This means that quite often if two characters have not been used together in a while, they may learn a Dual Tech or two when you do put them together.
Dual Techs have a variety of uses. They can change the element of an attack, adding one to a physical attack (as with Fire Whirl) or combining different elements into Shadow (as with Antipode). Dual Techs tend to be about as powerful as either tech would be used separately, so they are best used to exploit a weakness. They can also be used to change the targets of a Tech (as with Aura Whirl) or create an entirely new effect. Any given party not including Magus will have as many as nine Dual Techs available for use, so you'll have a lot of options.
There is one downside to Dual Techs (and Triple Techs) which is perhaps not that obvious: both characters have to have a full battle gauge to use one. In cases where one character is slower than another, relying exclusively on Dual Techs can actually slow your rate of damage. It is often useful to have the faster character take other actions while waiting, if they are fast enough. This fact also makes the game somewhat frustrating to play in Wait mode. On Active mode you can pre-select the Tech and use it as soon as the other character's turn comes up, but in Wait mode you need to stay outside the battle menu while waiting for this to occur.
Triple Techs
While Dual Techs are powerful and often useful, Triple Techs tend to be used sparingly. Any party that includes Crono and not Magus can learn a single Triple Tech. They tend to be dramatic and powerful, but since there is only one, they aren't always useful in a given situation. It's also a pain to learn them all, since you'll have to fight battles with 10 different party combinations to do so (and those after all the required Single Techs are known). There are five special Triple Techs which can only be used if one of the characters has the correct Rock accessory equipped. The advantage of these Triple Techs is that none require Crono, and two even include Magus. Of course, this means that you can't use them until late in the game on subsequent playthroughs.
The timing issue with Dual Techs is even more pronounced when you're waiting for the entire party to be ready for a Triple Tech. It's also worth noting that, despite most of them requiring Crono, there are no Lightning Triple Techs. Shadow is the most common element, because it represents any combination of other elements.