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How can I work out how high an aeroplane is in the sky from my position on the ground?

Arnav Guleria, Quantitative Derivatives Trader/Marke...

Visually:
One would need to identify some reference measurement, the wingspan, for example. This would require one to identify the craft itself. Then, the perceived length can be compared to the known length, corrected for atmospheric abnormalities, producing the distance.

(1) Calculate the size of the retinal image of a reference object:
0,17mm * tan[2 * arctan(Known Size of Ref Obj / {2 * Distance to Ref Obj})].
Note: 0,17mm is about the nodal distance to the retina.
(2) Calculate ratio of angular size of aeroplane to reference object.
(3) Use linear proportions to work out distance.

Alternatively, if one can use a theodolite to work out the angular size of the aeroplane, then one could do without the reference object and multiply 0,17mm by the tangent of the visual angle, yielding the size of the retinal image of the aeroplane, which could then be plugged into the equation in (1), solving for distance.

Range-finding, e.g. laser-based range-seekers.

When looking at an aeroplane in the sky, is there a way to locate it's approximate position over earth?

If you have an iPhone or other smart phone, there are a number of apps that will show active flights within a given radius of your current location. If you use that feature of the respective app at the moment you see your airplane, you'd be able to determine its location and identity that way. There is a free app for the iPhone put out by our company, Flightwise - Flightwise Flight Tracker Free is the name of the app.