The longest range hit scored by a battleship during WW2 was scored during the Battle of Calabria by the RN's HMS Warspite. Warspite landed a hit on the Italian Gulio Cesare at a range of ~26000 yards, or 24 km. To score a hit at such a great distance was quite a complicated business. You needed to know not only the range and bearing between the two ships, but also how they were changing. Then you needed to know how long your shell was going to take to reach the target. Determining the bearing was quite simple - look at the target, using binoculars, a rangefinder or radar, and see what angle it makes with the bow of your ship. Determining the range was somewhat more complex. By WW2, all navies used coincidence or stereoscopic rangefinders to determine the range to a target. These used the principle of parallax. Two separate images, as seen by either end of the rangefinder, were displayed. These would overlap, and form a single image, when the correct range was input. Radar was also used to determine the range. The Germans were the first to do it, with their Seetakt system being deployed from 1937. However, this system was very vulnerable to the concussion from firing the main battery, and so wasn't the most useful in a naval battle. The British Type 271, 272 and 273 (for escorts, cruisers and capital ships), deployed from 1941, and the American FC or Mark 3, again deployed in 1941, were based on the more resilient cavity magnetron. These systems had higher power outputs than Seetakt, and could survive the concussion of a naval battle. Radar was far more useful than a rangefinder, as it couldn't be blinded by smoke, could be used at night and in bad weather, and so on. To determine the changes in range and bearing needed four inputs: your speed and course and those of your target. Two of these were easy to measure, as you knew how fast you were going, and in which direction. Measuring the target's speed and course was considerably more tricky. It required a combination of looking at the orientation of the target's masts and superstructure, its bow wave, how fast it moved out of view of the range finder, and how the bearing to it changed as you observed it. Once you had all these inputs, they were fed into a fire control computer, along with things like the likely coriolis effect at the desired range, any effects from the weather and the rate of roll of the ship. The fire control computer was a complex analog device, which used cams, cogs, and electrical components to calculate a firing solution. The British system was called the Admiralty Fire Control Table, while the Americans had the Mk 36-38, depending on class. The firing solution was passed to the gun turrets, which were elevated and trained to the correct bearing and elevation. The guns were fired centrally, using an electric circuit. The fall of the shells from the first salvo would be observed, and used to correct the next. If shells fell short, the range would be extended. If the shells fell over, it was shortened.

As to who had the best, that's tricky. The fire control computers were generally quite similar, though the Japanese system didn't use gyroscopes to ensure that guns stayed trained and level. The main issue was determining the inputs to get a correct solution out. The Japanese, who mainly used rangefinders to determine range, had arguably the worst system as a result - they struggled in bad weather, and at night without searchlights. When they did deploy radar, it was of limited utility, being only accurate against a battleship-sized target. The Germans did have radar, but it was unreliable when needed most. The British and American systems were the best combination of radar and rangefinder, allowing true blind-fire, without any optical sighting. However, the superior quality of American gyrostabilization, and their use of remote turret control, probably gives them the edge. The American system was capable of maintaining a consistent solution while the ship it was on was undergoing radical maneuvers, such as back-to-back high-speed turns.