You can't use Company Actions until your FC is rank 5 (and rank 8 for the level 2 actions.)

You rank up by earning Company Credits, which act as both exp for ranking up, and also as a currency for buying actions and other items. They are earned whenever anyone in the FC does pretty much anything. Any time anyone in the FC does a quest, FATE, dungeon, craft/gather, etc, you get credits, so your FC will passively rank up over time (faster if you have more people in the FC to contribute.)