If you're providing all the information for the bones, then really this is more of a importer isn't it? The code is not really generating any content, it's simply displaying the content you provide.
Start with the simple case of a single bone. Make sure your code can read the bone specifications and draws the bone correctly (starting out with simple lines would be easiest, perhaps colored differently at each end?). Then move to two bones, ensure they line up the way you want. Then try adding bones that are to be drawn symmetrically. You could probably define these bones to have specific properties like what kind of joint they have, and if they are mirrored across the body. You could do some things to help visualize the data, for example drawing ball and socket joints as a sphere, and elbow joints as a cylinder.
If you're planning on animating this, you'll need to do a bit of work there. Likely you'd want to use inverse kinematics. The book Game Programming Gems 8 has a section on creating a "Non-Iterative--Closed-Form--Inverse-Kinematic-Chain-Solver" a mouth full for sure, but nevertheless helpful.
Even with a IK solver, you're going to have a very difficult time creating procedurally generated animations for walking/movement. As @Patrick Hughes mentioned, Spore is a great example of this challenge. There's a nice resource called Real-time Motion Retargeting to Highly Varied User-Created Morphologies that should help you start to understand the undertaking you have ahead of you. Make sure you take a look at the PDF linked on that page.
That being said, if you created an animation system that could do this, you'd have no trouble getting a job :).
I'll add more details on the actual drawing of the bones. First, let me define some of the details you'll have to keep track of, for each bone.
Bone start position - This is a 3D offset from the parent end position. For limbs and such, this would just be zeros, or at least small numbers, but it's better to have this information for things like ribs where the offset could be greater.
Bone line equation - I recommend starting out with straight lines, but you may want curved bones in the future (ribs, clavicle, etc). This information would include the bone length and direction. You'd use this information for calculating mid-point attachments to this bone.
Bone end position - This is a 3D offset from this bones start position. You'll need this for the starting point of some child bones. This can just be computed from the start position and the line equation. It's just nice to have to so you don't have to compute it every time you want it.
Bone connection type - There are at least one of these per bone, it could be a joint or something more solid like the ribs connecting to the sternum. You'll want this information at first to draw what the connection looks like, and maybe eventually to tell your animation system how this bone is allowed to move.
Your bones should be laid out in some sort of tree data structure. With the root bone (generally the hip or base of the spine) being at the root of the tree.
Start with the character position in 3D space. This is the starting point for all the bones, it's the root. Use this position as the offset for your first bone. The way the bones are set up, once you have the first position, you can calculate the start/end of every bone in the system. Once you have all the start and end positions of the bones in your system, you're ready to draw.
I'm going to assume you're starting with straight lines for bones.
Draw in whatever order you want, but you might as well parse the tree you already have set up. So start with the root bone, and draw it. This is as simple as drawing a line from start position to end position of the first bone. If you're not sure how to draw a line in your system of choice, I'd recommend taking a step back and deciding if you're ready for this project.
Continue parsing the tree and drawing lines from the start position to the end position for each bone. You may want to pull this information out into some other data structure for quicker drawing, but that's outside the scope of this answer.
I have to say though, from your responses so far, I think this project may be beyond your current skills.