* You have a Surface Combat TF with several BB, CA, and many CL/DD
* You have an Air Combat TF with three CV and many DD.
* Your adversary has the same on both counts.
Scenario 1: You spot his Surface Combat TF alone and don't know where the CVs are. What do you do?
Scenario 2: You spot his CVs alone and don't know where the BBs are. What do you do? Also, how do you maximize the results of a CV vs CV altercation?
Overall 3: Do you keep the BBs and CVs in the same hex at all times?
Overall 4: Would you send a BB task force off alone if you didn't know where the enemy fleets were?
Well, it's not easy to reply in general, as the real beauty of this game lays exactly in the details and specifics, but overal here is what I'd do (not necessarily the best tactics).
Scenario 1: no question, keep your SC and CV Tfs together in one hex, I generally put the SC TF in the lead with the CV TF following. in this case you're protected against a surprise nights surface combat and also have additional AA in your TFs. You can eve try to assign one or two BBs (or at least CAs) temporarily into the CV TF, 'cos only DDs means not too much added value against air attacks (well, unless we are talking about late 1944-45 USN DDs with anti-kamikaze refits).
Scen 2: Now this is where the specifics really start to matter. If you can afford to loose some of your SC TF ships and want to take a gamble, and have a direct line between your forces and the enemy CVs then I'd put my SC TF to max raction range (6) and plot a route to the enemy's hex with full speed. It's probably that a CV engagement will result the next turn and if you are lucky a surface combat will occure. I've done this in my PBEM against Juan, though I made a mistake. I went in at full speed and we got an engagement, bot both TFs evaded, despite having Halsey as my admiral. The problem was I had 2 or 3 of my CAs damaged by 250kg bombs the previous turn so they were not fast enough to catch the CVs, although they only had a really meager escort.
Generally this tactic is not bad to split the enemy's airstrikes as well, your CVs have a better chance of survival. Also you can apply long range CAP over your SC TF if you have enough fighter planes (this is really only an option for the USN later in the war).
Still I won't recommend this for rookies and it worth some tries against the AI before you do this in a PBEM.