Let me go into a bit more details because I need to vent about it :D
1. You cannot tell the carrier to join your Fleet, at best you can tell it to follow your Fleet and it will be part of battles.
2. To actually use it properly you need to switch your main ship from (probably Destroyer) to Gunship or Fighter and fly into its Hangar. It took me a while to even find it next to my whole fleet. When you enter it with your ship you can Pilot it from inside and then it can dock with bases so you can upgrade it and you can transfer Ore to it so it can also build its own ships. At this point you can mostly use it as a main ship that you never want to leave.
3. Now the fun part, if you want to do a mission that needs a craft that is neither Carrier or Gunship/Fighter you used to enter it good luck :D Now you need to exit it and as result you also leave the fleet and you are now a solo ship. For example I got a mission where I could only take gunship and 10 fighters. I could not even accept it while I was piloting Carrier. So I had to exit, fly into base with solo ship, take mission. Then I figured out that Gunship I used was not best one I had in fleet and I missed those 10 fighters. So I had to disband fleet and then tell everyone to join my new fleet and tell the carrier to follow it. Then I could go do mission and after finishing it, I had to fly into Carrier so again it becomes leader of the fleet.
When Destroyer was my leader of fleet (and all the times before), to do all this was one click in base that says change ship, then take mission, exit, do mission and game automatically removes all extra ships from fleet for mission and after mission one click to make your strongest ship your main again..
4. Best part.. you get to have one less Destroyer in your fleet battles as normally your main ship is not counted into fleet limits for battles.. this makes it so it is still worth more to have Destroyer as main ship while telling your carrier to just follow your fleet.. but if you do that you cannot make him build ships unless you manually fly into it each time with Gunship/Fighter (so more UI "fun" changing from Destroyer and back)
5. If you want to have multiple Carriers, you need to fly manually into each, then bring them to bases to upgrade them..
I also tried Remote Interface from a base.. that a story for another time.. lets just say you enter base with your fleet, go into remove interface and your fleet can no longer exit that base lol.. designer of this game was on some heavy drugs when he was designing these systems..
EDIT: I forgot to mention that maybe all this would be worth it if carriers were actually a beast (and maybe some from another faction would be) but you have less weapons than a Destroyer and get to launch 10 free weak fighters and you can make up to corvette Pirate ships that are all kind of crap and they are basic versions (also you cannot launch them during battles from what I have seen, you can only launch the free crappy fighters)