Cyan is essentially Sabin's best friend in the game. They connect out of convenience initially. Sabin had been separated from his party, and Cyan was the lone survivor of Doma after everyone else in his kingdom had fallen to poison in their water supply. Cyan vowed vengeance against the Empire, and began to attack it alone. This is when he ran into Sabin. Sabin suggested the two join forces, and it was smart, despite how strong and capable Cyan thought he was on his own. Sabin and Cyan started to rely on each other, and they made a hell of a team in battle.
While I think convenience sparked their connection, I think it's what they had in common that made them friends. The things they had in common made them close throughout the rest of the game, relying on each other even after other characters were in the picture. Cyan and Sabin had different back stories, but they were one and the same in a lot of ways.
I think the biggest thing they shared was a hatred for the Empire, and a desire to reap vengeance on it. They had both lost loved ones to the Empire - Cyan's wife and son, and Sabin's father for sure, and possibly his mother. What's more is Cyan's wife and son was killed by poison, and it was suspected that Sabin's father died because he was poisoned as well. Sabin and Cyan were able to empathize with each other. I think it's really awesome that they had each other, because while Sabin sort of had Edgar (They hadn't really talked in ten years.), Cyan didn't have anyone. I'm sure Sabin helped him a lot.
Although their connection was formed around such dark events, their interaction is pretty light-hearted. Cyan dislikes machinery, and as a result technology is not his forte. When Cyan has issues getting his Magitek armor to function, it's hard to tell whether Sabin gets frustrated, or makes fun of Cyan. It's funny, nevertheless.
I'm getting sick of this! Thou art such a pain in the...! Confound it all! I'm starting to talk like you!
The two seem to argue a lot, but it's obvious that they respect and trust each other. Cyan joins the Returners after Sabin asks him to, and Sabin keeps Cyan's shortcomings with technological knowledge a secret from the others.