Power Projection is mostly a naval concept and in essence means a fleets weaponry against land targets creating a zone where they die, they thus project (sea)power onto land. It can be used for other units and concepts (T2 art and TML for instance). Withouth power projection a navy(or anything) is essentialy useless like a fleet of subs when your opponent does not have any naval units.
However it is not only armed ships that can exert power the more powerfull variation is an aircraft carrier where the (air)power can be exerted more acurately and effectively then with ships, however the drawback is of course higher costs and vulnerablities of a carrier and the aircraft.
Below is a outline for a tactical scheme not necesarily related to an abstract concept like power projection.
Build your fleet. You should build 3-4 carriers, each supported by 2 cruiser, 3 destroyers, and 3-4 subs. This is rather expensive, so make sure you have a stable economy before starting.
Find the enemy fleet. This is best accomplished by scouts, and if you have any extra, subs. This is the most critical part of the strategy. Also, make sure you know the strength and whereabouts of the rest of the enemy ships, if there are any, but especially if you think they have another carrier.
Once you have located the enemy fleet, immediatly launch all of your aircraft, even fighters, to attack the enemy fleet. T1 fighters to draw fire, T3 fighters to ward off any enemy aircraft, T1 and T2 bomber to destroy enemy small and medium warships, T3 bombers to destroy any carriers or battleships, T2 torpedo bombers to destroy subs, and scouts to maintain a sphere of influence around the battle, to give warning of aproaching enemy reinforcements.
Send half of each carrier group's force ( 1 cruiser, 1-2 destroyers,1-2 subs) to finish off the enemy forces, making sure you leave enough forces for defense of the carriers, unless they are Atlantises, then you can just submerge the carrier and leave a sub or two with each one.
Recall all aircraft and ships. Have the aircraft land on the carriers and the ships move into escort position. But leave all or most of your subs behind. Bring your fleet back to base, and make sure they are well protected from attack.
Remember those subs you left behind. Well, chances are, that if your enemy had less ships, he would have sent them after you. So as his little fleet of, I don't know, a carrier, a battleship, 20 cruisers, and 20 destroyers, comes speeding along blindly, you ambush them. So they lose even more ships. Then, get your subs back to base before they get attacked by enemy torpedo bombers.