The rudiments are simple once you really look at what solid and surface features do
To begin with, Solid features ARE surface features, except: A) Solid features ALWAYS make a completely enclosed volume (which you can see in the preview for a cut, or if you deselect 'merge result' when making a boss then go to the solid bodies folder and hide the other bodies), while surface features are not limited by that constraint B) Solid features know which side of the faces it creates makes 'stuff', and which side makes 'void'. A surface sitting in space on its own, even if it does describe a completely enclosed volume, has no definition as to which side is 'stuff' and which side is 'void'. Is that surface a cylinder, or is it a drilled hole? It doesn't know until you tell it using 'thicken' or 'cut with surface'
I find it impossible to get caught in this rut about solid features vs surface features, and simply put it out of my mind years ago. They are different, yes, but only in execution. At the end of the day they both make the same thing - faces.
When it comes to modeling, the only thing that matters is faces. Repeat that to yourself - the only thing that matters is faces. When your product is being made on the shop floor, or when it is on a shelf/ delivered to a customer, the only thing that ever mattered was the faces of the object. That's what we do with our CAD - make faces. And our deliverables don't care how those faces were made.
Solid features make faces, but they always (well, almost always - there are spheres) have to make a few extra faces in order to follow the rule of delivering a completely enclosed volume. Which can be hard to visualize in the case of a cut... that's why I say look at the preview and you can see how a volume is made when you execute a cut, before it is subtracted behind the scenes from the 'workpiece' (otherwise known as that existing chunk of 'stuff' on your screen).
Surface features don't have that limit - you can make one or several faces at a time, then trim or knit those faces together to make the final model.
If you have the time, try to make a simple model one face at a time, using surfaces, to see how it works. Its horribly inefficient on simple cases (making a cube one face at a time requires 8 features, for instance - 6 planar surfaces, a knit, then a thicken enclosed volume), but you will learn how it works. That is what every 'solid' feature you have ever made does behind the scenes - solids are 'macros' for the tedious work of making things one face at a time out of surfaces.
But there are times when making model geometry one face at a time DOES make sense, and catapults you past problems that you run into when having to deal with that 'fully enclosed volume' restriction of solid features. There are samples on the Dimontegroup web site that talk about some of those problems, but apparently not clearly enough. Sorry 'bout that - I tried. As soon as I figure out how to rewrite the damn site there will be one more tutorial from this years SWx World that has (I hope) some of the clearest samples I have ever done talking about 'making faces'.
It's good to have surfacing knowledge in your magic bag of trix because there are times when doing things 'one face at a time' (or more probably, several faces at a time, just not as a completely enclosed volumes) with surfaces actually is wayyyy more efficient. Super mega wayyy more efficient.
And a lot of times, its the only way to get to the finish line - I have been using SWx for nine years, and I would gladly bow down, grovel, and wash the feet of the person who really can deliver on the statement that 'anything that can be done can be done in solids'.
A 'hybrid' approach (that is stupid slang for mixing surfaces and solids) is, in my experience and the experience of many others, the most appropriate way to go on certain projects. But again, bringing back to earlier in the post, I don't even think of its as a 'hybrid' approach because both surfaces and solids just make faces - if you pick features based on their ability to make the faces you need the most efficient way, there is no switching from one modeling environment to another. SWx is just one big 'making faces' tool. Cuts and bosses both make faces in different ways and we don't think of THAT as a 'hybrid' thing - why should we apply an arbitrary division to solids and surfaces?.
I hope this helped - I do not envy you for having to learn this stuff from the ground up. I am learning new software right now and am newly reminded how horrible it is to get straight, useful answers on fundamental issues that most people using the software have already come to terms with. Keep asking the questions, Amy, until you get an answer framed in a way that makes the breakthrough for you.
Ed