Hello there,
It is interesting that there are a lot of articles on magnets and magnetism and magnetic fields, yet the N and S poles are more rarely talked about. It's all about which end of the magnet the field lines emanate out from which end they go into. One is called N and that is because it 'seeks' the north pole of the earth, and the other is called S.
To be sure you have it right here is one simple experiment you can perform at home.
Be careful not to use too big of a battery or you could end up burning something or melting the wire or something else damaging.
First, wind a coil of wire around some cylinder like a dowel or something. Pay attention to how you wind it as to where you start the winding and end the winding, and what way you wind it, clockwise or counterclockwise as viewed from the top of the dowel, and mark the top of the dowel and top of the winding.
Take a brand new soft steel nail such as a 10 penny nail and place it inside your coil. Connect a small battery or other current source such that the positive terminal connects to the top of the coil, and negative to the bottom of the coil. That should magnetize the nail to some degree depending on the number of turns of the coil and the current that is developed in the coil.
Next, take a fine sewing thread and tie it close to the middle of the nail and maybe a little dap of super glue to hold it there, making the thread around 2 or 3 feet long (or around 1 meter maybe).
Then, hold the loose end of the thread so that the nail is suspended in mid air.
Wait until the nail stops rotating and see which direction the head points to. If it heads due north, then the head must be the N pole, and if south, then the point of the nail must be the N pole.
Now that you know the three things:
the direction of the turns of the coil,
the connections of the coil to the battery plus and minus,
the N and S pole of the nail,
you can then correlate that such that if you want to re-magnetize a magnet you just have to insert it into the coil or a newer larger coil in the same way as the nail, and make the connections the same, and if a new coil wind it the same.
You can also do this with a steel sewing needle but then you have to float it on top of a water surface or something to get it to rotate, maybe after sticking it through a small piece of Styrofoam.
I outline this procedure because there are so many articles that also get it wrong or leave out important details. By doing this you can ensure you get it right and you have all the details to understand all the polarities and how they relate to the N and S poles.
I've also seen several articles and videos by professors who neglect to show the entire experiment setup before the video is made, so they end up showing us absolutely nothing. You have to know all the details for something like this. This also happens with videos of experiments to show how the Lorentz effect works, and they end up showing us nothing.