Introduction and Disclaimer:
Believe it or not, each world/realm from the Northern tradition has a being or deity that symbolizes Death, or some aspect of it, and thus are what we refer to as "Ordeal-Givers". Ordeal work is work that involves the use of some extremity, generally pain (though emotions can be used as well) to achieve some goal. Some NTS shamans believe that to truly do ordeal work, they are called to experience each of these nine ordeals and meet with each of the Ordeal-givers. Whether or not that holds true for everyone, who knows? I think individuals who feel called to that work should attempt it.
But I do not personally recommend that people set out to do this work, as you cannot do it through willpower alone. I do not recomend this to anyone who is inexperienced in Ordeal Work nor do I recommend it to anyone without the consent of a doctor and someone to guide them through it. Safety is a must!
The way you go about this can be very individualized, and it does have some reflection on your practice. For instance, those who work closely with the Aesir and Vanir would wish to start from the bottom and work their way up, because they would end up working with their gods last and seal it with them. Rokkr workers would work from the top to the bottom, for similar reasons. Consider who you work closest with when you begin this type of work. (Helheim-Niflheim-Svartalfheim-Muspellheim-Midgard-Jotunheim-Vanaheim-Ljossalfheim-Asgard and backwards).
Obviously the Ordeal-Giver of Helheim is going to be.. Hel! Often ordeal work with Hel can be very in-depth and even more ordealish than a lot of other workings. It's not to be taken lightly. Ordeal work with Hel can, and does, involve physical pain. But Hel's ordeal also pulls upon emotions, such as fear, humiliation, and dread. Hel works best at terrorizing people to get them to open up, to show them the "scary" side of Death in order to teach them a lesson about it. As Raven K says: "The hallmark of Hela's ordeals is the moment of 'Oh no, I'm going to be killed now' or 'I can't take anymore of this or I will die'.". The purpose of Hel's Ordeal is to push you to the brink of your mortality, physically, and to show you the face of Death. She will use whatever technique she feels is nessesary to show you the flip-side to everything, and help you to see from her perspective. It is a great learning experience.
The Ordeal-Giver of Niflheim is Nidhogg. And Nidhogg is not to be taken lightly either! Niflheim is notorious for being seen as a shape-shifter to NTS shamans. Yes, Nidhogg does appear in the form of a great dragon- a form that is the most commonly seen one. But like any other Jotun, Nidhogg can assume other forms, and could appear however it wants to- even as a regular looking Jotun. Nidhogg is often assumed to be most closely related to the Frost-thurses, as its behavior tends to reflect theirs. If you have never worked with the frost-thurses, have never been exposed to them, or do not get along with them- you won't have an easy time working with Nidhogg. This ordeal will cause you to, quite literally, "face the dragon". Because Nidhogg is associate with frost-thurses, a lot of ordeal work with it involves the cold: standing in the cold naked, being coated in snow, jumping into cold water. But don't forget that Nidhogg is mainly associate with rot and decay. This lesson can teach you, like Hel's, that all cycles of life are important and should be respected.
Guess who? In this ordeal, you actually tend to view the Dark Alfar as the Ordeal-Givers, and generally it is their leader/queen who will give you the actual work. This ordeal often reminds me of the movie "mirrors". If you haven't seen it, you should watch it. Why? This work often involves broken glass, mirror shards, etc. Why? The dark alfar, in general, have a habit of breaking glass, of destroying objects and are quite fond of pointy things like knives. As you can imagine after hearing that, this kind of Ordeal tends to involve some kind of cutting, being stabbed or poked. Raven K suggests that the blood from this ordeal should be wiped on trees, and that you should not forget that the alfar are fond of song-magick. Singing galdr throughout the orderal is almost a nessessity.
I think this one is obvious as well. The Ordeal-Giver you will meet here is none other than Surt. Lord of the fire-etins, and one of the most powerful, oldest of their kind. He is not to be taken lightly at all, and often many are too scared to work with him simply due to his raw destructive power. Being a lord of fire, you can (hopefully) come to the assumption that this ordeal work may, perhaps, involve heat? And it does. Lots of it. Ever heard of firewalking? You should look into it. This work is really more endurance work than anything. Often it causes you to be uncomfortably close to fire, and have to perform some task while enduring the pure heat. Hot stones on your body while you meditate, firewalking, dancing next to a fire while doing intense ritual work, sitting in a sauana for hours, etc.
Angrboda is the Ordeal-Giver of jotunheim, though several Jotun are quite adept at pain. Angrboda is often a strong, indepedent figure and her ordeal work is often proving one's indepdent strength to themselves through some trial. She's very good at rage as an emotion, and often puts her followers through "hazing" ordeals. This is actually really common in Jotun, who will haze newcomers to see what their reaction will be. (Note: If you can't handle being hazed, don't go to Jotunheim. You'll be eaten alive. Literally). To work with Angrboda you may have to learn to control your emotions and to master yourself, allowing yourself to give in to your raw feelings will cause you to experience the pain that defines this Ordeal work. A fun type of ordeal work with Angrboda is the Hunt. Angrboda is an excellent hunter. So perhaps you may find yourself the prey being hunted. This plays upon emotions as well. Either way, this is an important lesson for the self.
This ordeal-giver can vary, depending on whether you intend to focus it on Earth or on Sea, as Vanaheim has two main focuses and two main ordeal-givers. If you intend to focus on Earth, you'll find yourself working with Nerthus, the Earth Mother. Raven K often describes Nerthus as the "embodiment of devouring Earth". As such the type of ordeal work you will do with Nerthus invovles being devoured by the Earth. You may find yourself buried in the dirt, treated as dirt, put in a large hole. Raven K suggests that there is a "full on John Barleycorn type of ordeal: one is treated as a grain is, scythed down with a a cutting, bound like a sheaf, beaten to symbolize milling, and placed in fire to mimic baking, before being buried in the earth".
If your focus, however, is the sea- Ran and her daughters will be the Ordeal-Giver(s). They are very adept at ordeal work, and often they are described as being particularly bloodthirsty. Depending on which Goddess you get as the ordeal-work, your work itself will be varied. "One such ordeal had the individual in question tied to a rope line, held by people on shore, and went out to battle the undertow as long as he could. "Dancing with the Sisters', it was called"(wightridden).
In either case, the lesson is to teach you about nature and its raw forces.
In Ljossalfheim, the Ordeal-Givers are Alfs. Some of the ordeal work you might go through here involves things like solitude, isolation, mental/emotional trials, as well as things like temporary madness. The Alfs strongly value these things, and that is reflected in their work. Unfortunately, outside of this, I don't know much on it. Like anything, it depends on which alf you get as the ordeal-giver, and what their particular talents are! There are several lessons about the self here. Some of this work can help you come to terms with your identity, and your mental capacities, or even bring up things you normally repressed. That is the point of ordeal work- to expose yourself fully.
This one seems obvious to me. Odin is the Ordeal-Giver here, which makes sense. He has a variety of techniques he uses to teach his followers through the ordeal path. However, some common ordeals with him involve hanging/suspension (symbolizing his hanging off the tree), runes being carved into the skin, or tattoos. The rites of Odin would fall under this category, so any of them would work as well. Asgard Ordeal teaches honor and courage, which makes sense as that is where warriors go. Expect to be put through a warriors test! Expecting anything less of that would be idiotic.
I left this as the last one to discuss because it is the hardest to understand. There's no specific Ordeal-Giver for Midgard. If you think about it, the person doing the Ordeal work is, in a way, their own ordeal-giver in this case. You will self-design the ritual. If you want to involve local wights, that is your call, but again- this ordeal rests on your shoulders. Remember what the point of ordeal work is: to open yourself up and be exposed. If you design an ordeal working that doesn't reach down and grab those deep emotions, there's no point in doing it! I often suggest getting a group together for this sort of thing. It's always good to involve the community, if you can. And it's nice to have others to watch and guide you through these processes. Raven K suggests that the Midgard ordeal should teach you something about humanity. Don't forget that while you are doing this spiritual work, you are still a human and you still are part of a society. Explore what that means a bit. Do some kind of work for another individual.