The capital ships gain additional squads as they level. Carriers tend to start with the most and end with the most, but some ships don't get a single one until levels 5/6.

There's nothing you need to do other than to feed them experience

Battleships and dreadnought-type vessels start with no command points. Battleships get theirs at around level 3 and dreadnoughts at around 5-6. Battleships have room for two squadrons at level 8.
Colonizers and utility capitals get a single squadron at default and get 2 at around level 5-6. Later levels have them end with 3 squadrons.
Carriers get two squadrons by basic and slowly gain even more as they gain levels. By the time one's at 10, it should have 6-7 command points.

Hope that explains everything for you.