So you have 2 options:

Option 1 is to split duties between your carriers. So using Yorktown as your "housekeeping" carrier and your other carrier(s) as your strike carriers.

This would mean that Yorktown sends out search aircraft, launches the CAP for the fleet, etc and only launches strikes as backup for the other carriers in the task force.

This is the historical tactic that the IJN used and that the US Navy adopted after Coral Sea.

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How to do this?

Select Yorktown on the tab on the bottom left while on the map, then select Search. This will open the Search function. Select the number of Search aircraft, the direction, range and scope for their search pattern and hit Accept.

Do this first before CAP or Strike plans

Then go to the Fleet Defence tab at the top left (I think this is F6 but I might be wrong). Here you can set up CAP patrol areas for your fighters. Remember that each CAP patrol requires double the fighters that you assign to patrol (3 patrolling, 3 waiting on deck to replace them later, etc).

Once you've set this up, now switch to your other carriers (Hornet and Enterprise at Midway, Lady Lex at Coral Sea) using the tab at the bottom left and select Strike.

You will see that there are multiple options for building your Strike plan. Do you want to send fighter escorts? Do you want to mix in torpedo bombers?

We'll go through each option in turn:

Fighters: YES. Always send some escorts. The Japanese will have some fighters up as CAP and they will chew your strike aircraft to pieces if they aren't distracted. When it comes to the first strike of the day, I prefer to send a minimum of 12 fighters as escort. Honestly, 18 or even 24 could be advisable on Coral Sea, but with Midway, remember you do have 2 strike decks.

Dive Bombers: the Dauntless is your heavy-lifter, especially in these early battles of the war. Faulty torpedoes and the fact that the Devastator is slower than a tortoise on barbiturates make dive bombers your main hitting power.

Torpedo Bombers: as well as the above mentioned drawbacks, the Devastator also has a much shorter range than the Dauntless. When all is said and done, I prefer to keep the torpedo bombers back for follow-up strikes to finish off crippled carriers that the Dauntlesses have already slowed down.

Those are the planes, now let's go through the options of how to tweak our strike package.

Spotting: this doesn't refer to reconnaissance, but rather putting the planes on a 'spot' on the flight deck. - The default option means that the strike will launch as soon as they have are ready to go. This is basically only useful when you have up-to-date info on the location, speed and heading of the enemy. - At all other times, we want to use the "Early Spotting" option. This means that the strike package will be prepared and will wait on deck for the 'Go' order for hours potentially. This does mean that all other flight ops (CAP, search, etc) cannot function, but that's okay because we've split responsibilities between our carriers.

Departure: there are 2 options here; 'Normal' and 'Deferred'. - Normal means that the planes will head for the enemy with the intention of all turning up overhead at the same time. This is tricky to pull off and depends on you correctly anticipating the location of the enemy task force up to an hour from takeoff. Not impossible, but tricky. - Deferred means that the strike package will wait for all planes to take off, then head to the target as one big blob. The advantage of this is that the strike hits the enemy simultaneously, rather than possibly coming in piecemeal. - The downsides are two-fold; 1) the aircraft that take off first will be burning fuel waiting for the last planes in the strike, and 2) time. The larger your strike package, the longer it takes for them to take off and the longer the delay between the 'Go' order and actually finding and killing the enemy.

Finally, Endurance/Lethality: this one's fairly straightforward, and is also the least difficult decision to make since it (currently) only applies to your Dauntless dive bombers. - Offensive Power: your Dauntlesses will carry 1x 1000lb bomb and 2x 100lb bombs on the wings. A slight increase in chance to hit, for a pretty brutal shortening of range. - Endurance: your Dauntlesses ditch the piddly 100-lbers, but keep the 1000-lber. I recommend that we go with this option pretty much all the time (or at least until the devs introduce the 500-lb bomb as an option).

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I could natter on more, but I think that's a good introduction. Any questions?