I think one of the good ways is for you to use party finder. Also, I believe you are looking for a Free Company. The Grand Companies are the story related companies like Immortal Flames. Free Companies are non-story related companies created by players.

To find the Party Finder, go to the main menu, then Party, then Party Finder. From there you can "recruit party members" and include that you are looking for an FC in the description. Hope this helps.