What's a chain attack and how do I do one?
I wouldn't worry about them too much until the game actually tells you about them, but... here's a primer:
A chain attack a special attack chosen from the menu at the cost of 'party meter' (same meter you use to resurrect fallen party members).
When the chain attack begins, time will freeze and all your party's cooldowns get reset. You will then get to pick an attack to do.
Based on a combination of random chance, your affinity with the next party member in the 'chain' and a few other factors, after the attack you MAY trigger a button prompt. If you get said prompt and hit the B button at the right time then you will switch to the next member and select an attack for them. This continues until the chain breaks.
While you are chaining, using an ability of the same colour as the previously used colour (or a grey as grey count as 'wild' as far as colours go) you will build up a chain multiplier. Depending on how high this multiplier is, the attacks used during the chain attack will have their damage increased (this also applies to Damage over Time attacks, like some that Melia has. This is what makes her beastly :3 )
There are various skills you can get that increase the chances of the chain continuing and, more importantly, some that even heal your party when a chain attack is completed. Get these as they're super useful :3
Early in the game don't worry too much about getting a chain modifier, but be sure to understand how it works... at the early point, the chains are really just an easy way of scoring a topple/daze but as you get further in you'll start getting the tools to really lay down some ridiculous damage and in some cases even generate enough party meter right after to do them almost infinitely :3