With that in mind, there aren’t many TF art tutorials because the fetish is particularly niche, but the furries have compiled some good resources we can build off of, my favorite being this tutorial: http://hippie.nu/~unicorn/tut/xhtml/
It’s long, but it goes through everything from basic geometry onwards. For what it’s worth, I’ll also link my Dropbox with a good collection of horse TF references. Again, can’t stress it enough, don’t worry about the PDF there if you’re just starting out; you have to walk before you can run. https://www.dropbox.com/sh/2m4ho5ofitx9hea/AAAAo-YMoqWJiljPLb3GZxEVa?dl=0

Once you have some pencil drawing experience under your belt, there are a couple ways you can go. If you don’t have a tablet, I think the most common is for artists to pick up a set of inking pens; they can be had for probably not more than 20 USD at a store like Michaels here in the states. You’re not looking to do calligraphy, so I don’t reckon you need anything too upscale.
Making nice lineart, much like making nice geometry, is a skill in and of itself, but it does make your art look all the more professional without a significant increase in cost. If you’d like to color the lineart digitally, you can scan it and it’ll look wicked nice as is; coloring it is probably different across platforms (Freeware: I’d suggest looking into Krita, SAI, and GIMP if you haven’t yet settled on a program; they have different tenets depending on what you’re trying to accomplish). The process shouldn’t be like pulling teeth; a simple Multiply or Overlay layer with your color should work nicely. If you don’t have access to a scanner, you’ll have to get tricky. I had a 5 megapixel camera on my phone (which is pretty standard for modern smartphones), and by playing with the brightness/contrast, and doing a bit of deft brushing, you can tease the lineart out.

Rendering is the other route you can go down early on, and I’m not even going to try explaining that right now; hit me up later if you’d like, because I can go for hours about even the basics of rendering. In a word, you’d be shooting for a fair degree of realism, and generally the lineart is either very light or nonexistent, and the shading gives a strong sense of form. Think Tsitra, Obpony, etc. Now, it definitely has its difficulties, but because it doesn’t require smooth lineart, it CAN be done WITHOUT a tablet – nothing more than a pencil, paper, a mouse, and your program of choice.

Hopefully that’s a good jumping off point; I’m not entirely sure whether I answered what you were hinting at. Everyone’s going to learn differently and a big part of the process is finding what works for you. And of course, art is such a broad, faceted field that you may never need to learn “x, y, and z” in order to become skilled at what you’re seeking to accomplish, while another artist may specialize in “x, y, and z” as their bread and butter. Best advice I can give is to enjoy the journey; drawing’s supposed to be fun!