As OneShot says, those are the sections to read. Once you've done that...
[EDIT - note that I'm going this late at night. So, I THINK I got everything correct...]
A Satyr with Magic Might of 22 (corpus) just means that he's got 22 levels of Might - meaning that any spell that affects him will have to succeed by at least 22 on the die roll (above and beyond what it takes to cast the spell) in order to affect him. So if you're trying to affect him with a lvl 10 spell, you're going to have to roll at least a 32. (base 10 + 22 penetration).
The "corpus" part of that just refers to what kind of magical creature he is categorized in via Hermetic Thought. Mainly this is used to figure out what kind of vis (magical power) you can get out of a magical creature if you kill him and take his stuff. And while all supernatural creatures are affected by Vim wards, they can potentially also be affected by a given Form ward. So in this example, the Satyr will likely be affected by both a Vim ward aspected to...Farie (if it's a Farie Satyr), as well as a Corpus ward. (Note that most consider the Vim ward more useful, as it affects a broader category of things.)
That troll has a Might of 5, so you'll have to succeed your rolls by 5 in order to affect him. The level of the spell itself doesn't matter, except that more complex spells require higher die rolls. As such, more powerful spells are less likely to penetrate. So in that sense most Ars Magica magical combat is opposite of (say) D&D - you actually use your Magic Missle spells to kill powerful creatures, rather than your Fireballs. (Unless you're really freakin' good at Fireballs, in which case you cast them whenever possible. Because what wizard doesn't like a nice Ball of Abbyssal Flame?)
Note that for clarity: Anyone with Might also has a (separate) might pool equal to their Might. This is the pool that magical creatures use to power their magic, and it fluctuates throughout the day. (ie, it goes down when they cast spells, and goes up when they rest.) This is temporary, and doesn't affect their overall Might score. So, their resistance to spells doesn't fluctuate over the day.
Some other interesting bits:
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Anti-Magic (aka "Perdo Vim magic") acts like you originally thought Magic Might does: that is, it automatically cancels out spells below a certain level. So if you've got a lvl 15 PeVi magical ward, you wouldn't be able to cast any magical spell up to lvl 15 into our out of that ward.
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There is also a variant of a Perdo Vim anti-magic ward that, rather than automatically cancelling out a spell, it simply drains the magical power of the caster. So, a lvl 10 version of this spell would subtract 10 levels of skill from anyone affected by it. This is like a negative version of Might.
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General wards (aka "Rego Vim magic") - supernatural creatures of the relevant realm (ie, Divine/Infernal/Magic/Farie) cannot cross the boundary of a ReVi ward. Note that these spells, like any other spell, have to penetrate Magic Might. So, that lvl 22 satyr would only be affected by a lvl 25 magical ward, with at least 22 levels of penetration (ie, if the caster rolled at least a 47 on the casting roll.) Note that over-penetration with wards doesn't do anything - so that lvl 25 ward will only benefit from 25 levels of penetration; anything more just doesn't do anything.
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Parma - this is what magi have. It's ALMOST identical to Might, but not really. Parma subtracts from any spells cast against the magi - to affect the magi, you'll need to have at least 1 penetration. However, because magi are mortal, they aren't affected by ReVi wards. Instead...
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Regular wards (aka "non-magical wards") - or wards that affect regular stuff, like water or rocks or (non-magical) humans. These don't need to penetrate, because regular things don't have any form of magical protection...except magi. So Magi are affected by "Rego Corpus regular person wards", but only if it can penetrate their Parma. Note that an object temporarily crated by magic (such as a lightning bolt or a fireball) is affected by both kinds of wards: it must penetrate a magi's Parma, but ALSO is affected by a regular ward. So, yeah - you can layer your defenses this way.
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Magi also have Form resistance - you add their level of a form (such as Ignem) to their Parma...or the other way around, I suppose. This means that magi always have at least a 0 in magical protection against something. This is useful because it's entirely possible to cast a spell with negative penetration - that is, (for example) hermetic magi can fail the spellcasting roll by up to -10, spend a fatigue level, and still cast it. However, they will be at negative penetration, so it may not affect their target.
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Aegis of the Hearth - is a funky beast. It's basically a triple-threat Ward. It is, simultaneously:
7a. acts like Magic Might, covering the entire covenant with magic resistance up to its level. Spells that cannot penetrate simply fail to do anything but bounce off the shield. (This does not stack with other forms of magic resistance.)
7b. A general RegoVim ward that affects all four Supernatural realms. (this needs to penetrate)
7c. an anti-magic ward that subtracts half its level from any spell cast through it. (this does not need to penetrate, as it affects the magic cast, rather than the caster.) This functionally stacks with Parma and other forms of magic resistance.
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you CAN affect a supernatural creature's permanent Might with a Perdo Vim might stripper - such as "Demon's Eternal Oblivion", or the realm-specific version. Yes, this means you can melt down that satyr with a lvl 5 Might Stripper, just by plinking him with it 5 times. This is considered a perfectly valid strategy for dealing with supernatural threats, assuming you can somehow set up the scenario so that they don't chew off your face in the 5 rounds it takes you to cast it. (Hint: use spell Mastery to multi-cast.) Note that doing this will prevent you from harvesting the body for Vis, of course - you just melted it all away.
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The Penetration ability - standard penetration is calculated just by taking the remainder of your roll, after you cast the spell. You can ADD to that using the Penetration ability. The formula is as follows:
Penetration = (Whatever is left over after you cast the spell) + (Penetration Ability)*(1+ Arcane Connection + Sympathetic Connection). This is described (very poorly) on pg. 84.
In this context, you don't need to use the Arcane Connection range of a spell to use an arcane connection as a bonus to your penetration. Rather, if you have an AC to the target, you can use it to boost your penetration of any spell cast on them. It just so happens that Hermetic magic allows you to ALSO design a spell that lets you hit them wherever they are, if you've got one. Of course, if you've got an AC, and are using an Arcane Connection range, you can ALSO use that AC as a penetration multiplier.