In magnetostratigraphic logs various chrons are distinguished with either normal or reversed polarity, with the magnetic north pole at the geographic north and south pole, respectively.
How and why can these polarities be determined? Note that I'm not after the quantummechanical reasons for magnetism, but how rocks store the magnetic orientation and how this information can later be retrieved from the rock.
This is a big question: it essentially translates to ‘how do we do palaeomagnetism’? I will try to give a brief overview and links to more detailed explanations. I'm also going to focus on the ‘how’, and leave the ‘why’ to someone else (perhaps it would be best split out into a separate question?). To record the geomagnetic field, you need three things:
There are a surprising number of ways that (2) and (3) can happen, but for this answer I'll just describe the two that tend to be most useful: thermal remanent magnetization (TRM) and depositional remanent magnetization (DRM).
Thermal remanent magnetization is induced when a rock cools from a hot (often molten) state. Here, (2) occurs because, above a certain temperature called the blocking temperature, the magnetization of a mineral is able to change freely to align itself with the earth's magnetic field. As the rock cools, it becomes harder for the magnetization to align, and eventually it is locked in place.
Depositional remanent magnetization occurs in sediments, and is induced when grains of a magnetic mineral fall through the water column and land on the sea floor (or lake bottom). While they are in the water column, the grains are free to move and align themselves with the geomagnetic field. Once on the bottom, they gradually become buried in more layers of sediment, fixing their original orientation.
In principle, recovering the recorded field from a piece of rock is very simple: you record the rock's orientation, cut or drill it from its current situation, then measure its magnetic field in a laboratory magnetometer. In an ideal world, the field you measure would correspond to the Earth's magnetic field when the rock was formed. In practice, it's rarely that simple, and you might need to use heat treatment or alternating-field demagnetization to ‘peel off’ weaker magnetizations that have been layered on top of the original magnetization over the years.
This answer is a gross simplification and glosses over a great deal of theory, practical detail, and possible complication. For more depth, I would direct you to two excellent textbooks which (thanks to the magnanimity of their authors) are freely available online:
Tauxe, L., Banerjee, S. K., Butler, R. F. and van der Voo, R. (2014). Essentials of Paleomagnetism, third web edition. http://earthref.org/MAGIC/books/Tauxe/Essentials/ (accessed 2014-04-17)
Butler, R. F., (2004). Paleomagnetism: Magnetic Domains to Geologic Terranes. electronic edition. http://www.geo.arizona.edu/Paleomag/book/ (accessed 2014-04-17)
Tauxe et al. (2014) is more recent and more extensive; Butler (2004) is an electronic reprint of a 1992 book, but is still an excellent introductory work, and provides (to my mind) a slightly gentler introduction than Tauxe et al. (2014). (While many advances have been made since 1992, the basic theory and techniques have not changed.)
If you are interested in the nitty gritty of how the techniques are actually applied, you might want to look at:
Richter, C., Acton, G., Endris, C. and Radsted, M. (2007). Handbook for shipboard paleomagnetists. ODP Technical Note 34, Texas A&M University, College Station, Texas, USA: Ocean Drilling Program. http://www-odp.tamu.edu/publications/tnotes/tn34/TNOTE_34.PDF (accessed 2014-04-17)
The paleomagnetic field is recorded initially by minerals with a magnetic dipole, which is lined up with the surrounding magnetic field as long as the temperature is above the so called Curie Point. When these minerals cool down below this temperature the dipole is 'frozen' and fixed until the mineral is exposed again to a higher temperature. Different minerals have their Curie Point at different temperatures, so you'll seldomly find a rock with a single paleomagnetic orientation.
To later measure this orientation most often sample cores are drilled from the rock, carefully recording the original orientation of the core and analysed in a magnetometer. This device is shielded from the surrounding magnetic fields which are invariably stronger than the magnetic dipole stored in the sample. By either heating the sample or exposing it to a electromagnetic field the magnetic field in the sample is detected.
After this is determined one must carefully reconstruct the paleoorientation of the sample at the time the magnetic field was captured, by reconstructing the tectonic history of the sample, which might include regional folding or faulting, or rotation of plates.