So yes, you're right that for much of the war, shells used a timed fuse. This set the shell off after a given length of time. However, this time was not fixed; it could be changed, so that the shell would detonate close to the target aircraft. This was combined with the other fire control calculations needed to get the shell near the aircraft. For most of the war, these calculations were done using a device called a 'predictor' or 'director'. These were electromechanical computers that could calculate the path of an incoming aircraft. This could then be passed, through cables, to the guns. Here, a time fuse was set according to the calculations of the director; this could be done manually or using another device called a 'fuse setter', depending on the gun. Later in the war, the Allies introduced a 'proximity fuse'. This used a miniaturised radar in the nose of the shell to detect an enemy aircraft nearby. This meant that the shell could be detonated at exactly the right moment, and therefore was much more accurate and effective.

The Royal Navy's main AA director during WWII was the High Angle Control System, or HACS. To engage a target aircraft with HACS, the ship's Air Defence Officer on the bridge would designate a target with an air defence sight. This cued in the Director Control Tower (DCT) to the target's location. The DCT would track the target, measuring data about it. It mounted an optical rangefinder to measure the range to the target. Later models added radar systems to make a more accurate measurement of range. The aircraft's course could be determined using its angle relative to the ship. The speed of the target was estimated by the personnel in the DCT. These data were passed to the Transmitting Station, which housed the ship's fire control computers. Here, a 'High Angle Calculating Table' would crunch the numbers, and determine the correct direction to point the guns and the fuse settings. These were then sent to the guns. The gun crews would read off the azimuth, elevation and fuse setting from dials which tracked the HACS results. The guns were then trained and elevated and the fuses set manually. HACS was a fairly good system, but had several major flaws. As originally designed, it was intended to track and engage a single aircraft; it could not fire a barrage at a given altitude and position. This made it hard to use against dive-bombers in particular, though there were work-arounds. During the war, a barrage unit was developed and added, which greatly simplified the use of this essential tactic. HACS was also less accurate than its equivalents in other navies, the USN in particular. HACS relied on estimates of the target aircraft's speed, and assumed that the target's speed course and altitude remained constant. Other navies systems were 'tachymetric' - they relied on actual measurements of the target aircraft's speed. This made them more accurate than the British system, if the other inputs were comparably accurate.