As I recall, you cluster partnered characters into 3 groups. Within these teams of 2, you can only choose to select an action of 'one' of the characters in battle, and the AI will play out a scripted action for the other character(usually they just run up and attack blindly outside of a few special cases, you have no control over what the AI does). So if you choose healing magic for team A, the partner that casts will do just that, while the other one will just run at enemies and kill stuff. The game leaves it all up to you to experiment with different teams to see which kill indiscriminately, and which hold guard over their partner. An icon or something would have been nice to help out with this, but just assume that whatever partner you DON'T select an action for, will end up run blindly into melee combat.
Let's see, items can ONLY be used on the actual partnered characters, if you want to heal a different pair only magic can reach them(unless there were special items that healed the group...I forget).
Magic takes time to cast, melee attacks require your characters to not only take a certain amount of time to run up to your enemies, but also to swing their sword/axe/dagger/etc.... Not too different from Grandia really, there was a small bar in the bottom of the screen that kind of helped gauge whether your actions would take 1-turn, 2-turns, 3-turns or more to actual complete. Unlike Grandia, there was no corresponding meter showing what the enemies have planned, so the whole thing sort of felt moot outside of displaying magic charge langth. Melee combat never really took great advantage of the system as I remember. You rarely if ever need to focus on that chart at all.
Oh and you CAN upgrade skills with points earned in battle to lessen the amount of time it actually takes melee fighters and casters to actually unleash their attacks. But again this system really added little to melee combat depth, and only magic got real use out of it(casting spells can go from 2-turn charges to insta-unleashing). Melee got some mileage out of the accuracy, combo, and damage upgrades tho...
The support character is a 7th character slot that confered bonuses on the party. Better magic damage and crap like that. They never fight or are seen on screen IIRC, just bonus adjustments for the party of your choosing(dependent on character selection).
It's not all that complex really as I remember it, just needlessly convoluted while providing little reward for thoughtful planning. The AI junk was just annoying moreso than interesting. In the end, this IS still a Suikoden game; and much like the previous 2 entries, auto-combat will probably get abused the most. This series is not really known for invigorating battle strategy.