Bring up the Ship Info Screen, then mouse over the colored dot marking a main battery weapon. If it's got a director, it will say "central+director" down in the lower text area where you see the other stats for the weapon.
At the start of the 1915 campaign, most ships DO NOT have directors, so to make things easier for you, I'll just list the ones that do:
RN: The Iron Dukes, the KGVs, Neptune, Thunderer, Tiger, and (surprisingly) Redoubtable. Pretty much all BBs and BCs that arrive as reinforcements have them to start with, and of course all the refitted capital ships once they return to play.
German: The Konigs, the Kaisers, Blucher, and newer CLs from the Magdeburgs on.