Armadas you get once you reach about level 23 and you unlock the Armada Control Centre Building.
Initially you have 2 spot Armadas, and need to level the building up to accommodate more first 3 at Building Level 10, 4 @ Building Level 20, 5 @ Building Level 30, 6@ Building Level 39 and finally 7 @ 50.
At lower levels your best bet is to get a big hitter/hitters on your alliance to assist in the armadas so you can hit higher value targets to get more credits to buy the Armada Tactical Cores you need to upgrade the building. So with 2 for example hit level 25 Armadas with one spot for a heavy hitter 600K+ ship, when you have 3 spots move up to 27 level Armadas, and so forth.
This should help to get more credits to speed up the levelling of the building.
Rough rule of thumb on Armada’s is to have a strength of about a 1/3 of the Armadas strength. so if 2.8m armada you want near the 900K mark to be successful. Some Armadas are more difficult than others, you should check out the stats to see what the damage and health of them are, non-faction ones tend to be a little easier than faction, and eclipse have a different dynamic altogether (covered in Rogue).
Buy Tactical cores from the Alliance store from initially the Uncommon Armada Pack and then if you have spare the Armada Tactical Cores so you can increase the amount you get with each purchase and cool down periods.
Rare Armadas require Rare Amarda directives, and you should try not to waste these. You can gauge the level you should attempt based on the Alliances strengths and past history. They are quite a bit more powerful than uncommon Armadas and the same rule of thumb roughly applies. Do try to hit as high as you can to maximise return on credits, which are then used in the Alliance store to get the Rare Armada Packs. I try to save the circa 7000 credits to get 6 chests in one go, as there is a 24hr cool down period once you buy.
Very much like the Rare, and the uncommon before, from experience, and strength of ships in the Alliance try to maximise the return, Marauder and Pirate Armadas can be good for this at lower level as the have 2.5m Armadas in Narendra, 7.2m in Pirate Stonghold Niawillen and 12m in Afritalis. Build up to these as you progress and get more slots on each Armada, I would recommend 5 as a minimum for the Afritalis ones and higher level ships for Faction Armadas at similar levels.