Basic (SE Stuff):
Vana'diel Guide's The Art of War
Advanced:
Killing Ifrit Skillchain Guide
Summoner:
[See What is a Renkei?]
Basically, you can perform a level 1 skillchain (Detonation, Scission, Liquefaction, Impaction, Induration, Compression, Transfixion, Reverberation), a level 2 skill chain (Fusion, Fragmentation, Gravitation, Distortion), or a level 3 skill chain (Light, Dark). You may only go "up" in a skill chain sequence not down, so you can't get a level 1 off a level 2. Only more powerful weaponskills can hit level 2 or level 3 SCs. These higher tier SC's have either 2 elements (level 2 SC) or 4 elements (level 3 sc) associated with them for Magic Burst and for the elemental effect vs. the target mob. SCs are very complicated and there are several charts available:
Destiny Seekers Renkei Chart Aden's Renkei Chart
The first one is (IMO) easier to read, but the second is more complete. I have both printed out. Aden's fancy graphic crap doesn't play very nicely with my printer.