You need to learn the very basics of drawing, preferably of art in general. If your artist friends do not have the balls to tell you this, then shame on them. If you have the means but are not taking basic art classes, shame on you. If you don't have the means to, that's rather unfortunate, and I am sorry.
In the case that you simply want to draw your characters, you need to first understand the media you are using, and then anatomy and proportion.
With a pencil, work across a heavy range of values (lightness/darkness of an object) and get used to creating varying ones. I would suggest drawing a series of boxes across the paper, one side being as light as you can possibly make the pencil and the other side as dark. This practice will help you with control over how you're laying down the graphite/lead/whatever-they-make-pencils-out-of-these-days.
Also work on making long, smooth strokes with the pencil instead of short, jagged/hairy lines. Throw your arm into it, get used to drawing big. Restricting yourself to a tiny space is only going to cause harm to your wrist in the future, and restrict your ability to draw larger in the future. Amongst galleries, all the rage right now is having ridiculously huge paintings, but I digress.
Just really get used to your pencil. You don't have to sleep, or dine, or love on it or anything, just know how to use it.
With anatomy, start basic. You're drawing anthropomorphized critters, they will most likely have a basis in humanoid (thus human) anatomy. Study the skeletal structure, how everything looks and works with every other portion. Move onto the muscular system, how they connect to the bone, how they overlap or connect to each other, and how they move under different circumstances (ie, bringing your forearm up causes the bicep to 'relax' and gather up and the tricep stretches, whereas holding the arm out straight causes the bicep to stretch out and the tricep and the fat around it to form ungodly underarm wings). Get an idea about the basic layout of fatty tissue around the body, then move onto flesh, how it lays across the fat, muscle, the bone.
Once you have an understanding of how the skeletal and muscular system works, it is a lot easier to make very quick studies of animal systems and combine them with a human structure. Of course, furries are relatively easy to please, so as long as you have the cookie-cutter furry form down, all you really need to work on is the structure of the skull of any critter that isn't canid.
Also, it sounds like a lot more work than it is.
In any case that you actually care about art in general, learn first the elements of art (link 1 and 2 at the bottom), what their purpose is and how you use them. Study each one individually. I would suggest taking at least a page up in a sketchbook on each one, and rewriting them - in your terms if possible - so that you better remember them.
And in any case you need help on them I am around and can elaborate on their functions.
After that, you should go about learning the principles of design (link 1 mentions them, link 3 leads to them directly). The seven that I learned back in der school of high were Unity, Repetition, Variety, Emphasis, Proportion, Balance, and Contrast. They should be listed in the links, but in any case they're not explained well, I can also aid with that.
http://www.msdsteuben.k12.in.us/jrider/elements_and_principles_of_art.htm
http://en.wikipedia.org/wiki/Principles_of_Design#Elements_of_Design
http://en.wikipedia.org/wiki/Principles_of_Design#Principles_of_design