Basically, how can we measure the Earth’s rotational axis accurately enough to be able to erect a physical [pole](https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Fantarctic-logistics.com%2Fwp-content%2Fuploads%2F2016%2F08%2Fdestination-south-pole-1.jpg&f=1&nofb=1) that goes through it? And how did expeditions in the early 20th century know when they successfully reached the poles?
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Early expeditions likely used the magnetic poles. Failing that, however, we know the locations of the poles relative to the magnetic poles. Using some geometry, we can find the direction to the actual pole if we know roughly where we are and what direction the magnetic pole is in. As to how we can precisely measure the poles, the simplest thing I can think of is the [gyrocompass](https://en.m.wikipedia.org/wiki/Gyrocompass) . This is a device that measures the rotation of the Earth and uses it to tell us what direction North is.
From the best I can find it is a mixture of using nautical and aerial charts and a sextant to accurately measure the Latitude and Longitude using celestial observation. The navigation was verified later by looking at the recorded sextant data and checking it with charts. The first verified successful attempt for the north pole was in 1926 by aircraft.
Before radionavigation such as GPS people mainly used dead reconing and celestial navigation. Dead reconing is when you measure the direction and the distance you travel and plot this on a map to find out where you are. If you look at some images of the polar explorers you might see that they often leave a wheel trailing behind them which have a counter so they can count how far they have traveled. When they are stationary they can use celestial navigation which is done by measuring the angles to different celestial bodies such as the sun, moon or stars to the horizon at different times. This is done by the use of a sixtant or octant and a good clock. The first mission to the South Pole spent hours on the pole making celestial observations to make sure they were in the right place. A third technique of navigation which could be used on land was triangulation. This is when you measure the direction to known landmarks so you can plot your position on a map. This was the most accurate way of navigation but only works when you are in an area of mapped landmarks. Also to note is that even with highly accurate GPS technology all these older methods is still being used either as backup to GPS as they are more reliable or as primary systems because they are more accurate.
Latitude is easy to work out with a sextant. An almanac will tell you the current declination (latitude) of the sun (or other visible object) and you can measure how high it appears above the horizon with a sextant. Close to the pole you don’t even have to wait for noon. With practice it’s not too hard to do better than a mile in accuracy. You won’t have a sea horizon but you’re on land or ice so you can use an artificial horizon (measure the angle between the sun and its reflection on a liquid surface).
You can measure your latitude quite accurately by observing the position of the sun at noon. Using a sextant and an almanac, you can get to within about a tenth of a mile.
As for physical poles, they are just a decoration, you get it close enough and call it good.
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