I don't know why it's secret, exactly. Travel time is effectively Distance / Speed, where Speed is a function of Hyper speed of the ship and your piloting skill. Exactly what weighting the Hyper and piloting skill get are the secret part.
XP = A * Distance Travelled, I don't recall what A is. 5XP per square or something.
Distance is calculated as Jev mentioned, a series of 90degree straight lines and 45 degree angles. (You can see this visualized in the City/Terrain travel where it shows a series of 45-degree moves to the adjacent row/column and several straight paths. NaviComp uses the hypotenuse, I believe, which is why it's often Off from the real times.
If we assume it'll always make you move 45 degrees when you can... I think you can approximate the calculation as follows:
point A (x y) to point B (x1 y1)
deltaX = abs(x - x1)
deltaY = abs(y - y1)
maximum path covered using 45 degree angle hops only = Min (deltaX deltaY)
Distance1 = sqrt( 2 * Min(deltaX deltaY)2)
path remaining to go is then just a straight line of length Max (deltaX deltaY) - Min(deltaX deltaY)
So Distance 2 = Max (deltaX deltaY) - Min(deltaX deltaY).
Total Distance = sqrt( 2 * Min(deltaX deltaY)2) + Max (deltaX deltaY) - Min(deltaX deltaY)
Can probably simplify that, but I'm lazy.
Time = Distance / Speed
Speed is (maybe) something like HyperVal * (a + b * PilotSkill) or maybe a * Hyperval + b * PilotSkill. You'll have to fiddle with the numbers and get some experimental data to try to approximate it if you really want a 'good enough' equation.