I'm in a phase where I'm very interested to read about air warfare in western Europe in world War 2 (hopefully I will expand to the eastern front as well in the future). I read on secondary sources that often navigation in bombers was difficult, there were electronical devices to improve the navigation, but still mistakes were committed.
The navigator in the airplane had only to handle the electronical devices or also had accurate maps, rulers, and so forth to establish the position of the plane on a map through computations?
Can anyone explain their procedure (or link it) if they had to determine manually the position of the plane or if they relied on devices and precompiled tables? (like 'if you get the signal x, look in the precompiled map that we'll tell you the position related to the x signal' )
Mostly map work and instruments - at least early on - which is why the Blackouts actually worked as a measure to reduce the accuracy of Bomber attack. There are examples of long-range guidance by electronics; however, the Luftwaffe used radio transmitters and modified Lorentz blind-landing sets (short range radio receivers designed to guide pilots in to land in poor visibility) to produce the 'knickerbine' bomber guidance system.
The system essentially consisted of a radio that would pick up either dots or dashes if you strayed too far left or right of your flight path and a final beam that told aircrews they were over their targets. The system relied upon the fact Germany controlled France and Norway, so they could properly cross all the beams of radio signal required. The system was not incredibly successful because local interference (such as falsifying the signal for 'you are too far right' at the rightmost edge of the lane) could cause it to mislead the pilots it was supposed to lead, and it was rather expensive (directed high-power radio transmitters aren't cheap).
Early war navigation was a manual affair in the RAF using techniques such as astronavigation (taking a fix on celestial bodies with a sextant) and dead reckoning (using airspeed and direction). This wasn't particularly accurate at night, meaning RAF bombing was inaccurate; the Butt Report of 1941 report famously concluded that only one in three bombers got within five miles of their target.
The Luftwaffe had adapted the Lorenz blind landing beacon into a navigational aid for bombing called Knickebein used during the Blitz, with one beam guiding bombers towards a target and a second intersecting beam indicating the bomb dropping position. As noted, when the British learned of Knickebein they began a programme of jamming or bending the beams to limit their usefulness. The Germans developed improved beam guidance systems, X-Gerät and Y-Gerät, though they in turn were also jammed.
RAF navigation steadily improved, with devices such as an electromechanical Air Position Indicator for more accurate dead reckoning, and their own beam navigation systems: GEE, Oboe and Gee-H. They also employed H2S, centimetric ground scanning radar that gave a crude picture of terrain.
There was an RAF Historical Society seminar on [A History of Navigation in the Royal Air Force that may be of interest] (http://www.rafmuseum.org.uk/documents/Research/RAF-Historical-Society-Journals/Journal-17A-Air-Navigationin-the-RAF.pdf). Most Secret War by R V Jones is also a very readable account encompassing the "Battle of the Beams", though focused more on the technological side of things rather than the navigational.
Some other useful material on the web:
My grandfather was a navigator in the Argus doing navigation by hand was a thing for quite a while. He showed me the textbooks he used when he was teaching navigation in the 50s. Mostly trig in base 10 I'll see if I can find the book in the morning.