Like I said Strac, only the three sites.
Addenak keeps the chart updated (the one above is 2.1, the current is 4.2+ - many MANY changes happened - but the SC chart doesn't concern you much - it is for the Samurai to memorise).
Currently being updated with Aht Urghan skills so it changes quite frequently.
What's a Skill Chain? Basically, two Weapon Skills or more. Weapon Skills are what melee fighters get when they maul enough with their weapon (similar to your Black Magic status increasing with use of the magics). The Weapon Skills (henceforth WS') are all different for all types of weapons, and they do one or sometimes two elements of damage, depending on their position in the SC.
So, as you can see on that list - if a Samurai with his Great Katana uses Tachi: Enpi and that WS is followed by the Small Axe's Rampage, the resulting skillchain is Distortion, which carries the elements of Ice/Water.
There are 3 levels of skillchains.
Level 1 is a Skillchain that carries only one element.
Level 2 Skillchain carries two elements.
Level 3 Skillchain is special, and reserved only for high level weaponskills (which is near endgame).
Basically, no matter what anyone tells you, you want to go for the Level 2 skillchains at all times. Why? The Magic Burst.
Skillchains by themselves, unless the following WS after the first one does a lot of damage - are useless. The thing that it is important for is the Magic Burst that Black Mages and high level Red Mages can do.
Which is why it is best to do a Level 2 skillchain. A mage has the choice of doing a magic burst with TWO spells instead of only one. Plus, Level 2 Skillchains do 65% of the second WS damage rather than 50% which is a story not meant for you.
A bunch of level 1 skillchains which you do when there's no SAM around.
When SAM is present you do the following:
Distortion you can MB with Ice and Water spells
Fusion you can MB with Fire and Light spells
Fragmentation you can MB with Wind and Lightning spells
Gravitation is with Dark and Earth spells
Usually, it's just Distortion, because mage has high Blizzard and Water spells earlier than other ones, and most monsters take a heavy beating from those elements.
So, how do you time it?
People usually do this in seconds. And for a Black Mage, I assume seconds for countdown are important. This is how everyone performs an SC:
One guy does the first Weapon Skill - Second guy waits for the first weaponskill's animation on the monster to finish, then he starts his weaponskill. If they did it withing 3 seconds of eachother, one after the other (after animation finishes from the first), the animation for the SC will start and 50-65% of the damage from the Second weaponskill will be transfered to the mob. Naturally if the mob cons to the element with a defensive resistance, the damage will be lower.
This is where the BLM comes in. After the SKILLCHAIN ANIMATION finishes, the mage has a 1-2 second window to get his spell in. If the spell is cast within 2 seconds after the SC animation ended, you will Magic Burst automatically.
How to time it? For the low end spells that you're using, know how much it takes you to cast them, and learn how much time it takes for the second WS and the SC animation to finish.
The Second WS Animation lasts for 5 seconds. The SC animation lasts for 3 seconds. Your spell needs 4 seconds to be cast.
You count the five seconds from the second animation, and as soon as that's finished, you start casting your spell. Cast time counts down, the SC animation finishes and your spell is cast performing a Magic Burst.
Fairly simple once you get the hang of it, but that is until Ancient spells come in like Freeze which take 14 seconds to cast - then the person who's starting the skillchain needs to time it to YOUR spell and not the other way around like it's normally done (but we'll get to that when you're level 40+)
I hope that clarifies it somewhat.
Oh and education - why is Samurai the Skillchian Master? Samurai's WS' are all over the board with different effects - we can close and open almost all of them with our weaponskills, as you can see in that chart there. Samurai also gains TP the fastest in the game (if he has freaking +acc gear and is able to hit which isn't my case because the shit's expensive -_-) then he can skillchain twice with two melee's in the group, therein giving the mage the opportunity to MB twice - more MB's, more damage, mob dies quicker.
Hope that explains it somewhat.