These are the things that when they are done, no matter in what language and with what rendering engine, you can consider yourself a semi-expert on this matter.
Build your own custom graphic initialization function
Today with the great variety of 3D engines and platforms, this task is always delegated to those. I still remember the times when you had to initialize openGL with all the windows functions, and how you had to manage windows handles and resource loading yourself. This is useful to understand how things are managed internally and will give you more comprehension of what you are doing. My advice is to start looking at NEHE tutorials, it has a graphic initialization function written in C and with windows APIs in chapter one. If this is a lot for you to handle, you should look at C++ equivalent functions or try to port them to managed languages like C#, Java or Python. There are plenty of examples on the internet.
Implement your own camera
You can copy and paste a camera code from the internet, and use it without major problems, but it is not until you make your own camera from scratch that you will fully understand some concepts like vector handling, translation matrices, angle conversion, etc. You should start by coding a FPS (First Person Shooter) camera; it has everything it needs to get you ready. Later if you want to make your own game and you can't use it, I recommend you to read this article to find out the type of camera that best suits your needs.
Understand primary 3D concepts
When I started, I began to hear a lot of new words like, anti-aliasing, anisotropic filtering, occlusion testing, z-buffer, alpha testing, shader language, bump mapping, etc. Maybe if you are a gamer, you have seen some of them while configuring the graphic settings of your game. Make sure you spent some time reading about this, because it will give an overview of what 3D programming is.
Learn everything you can about vectors and matrices
This is always underestimated, I strongly recommend that in order to correctly manage things like cameras, terrain following, ray tracing; you should know everything about this. You should also learn minimum trigonometry basis. Now I understand how easy my life would have been if I would had spent only a few hours studying this matter.
Code yourself a 3D model loader
I recommend to begin with a .OBJ file or a .STL file because they have an ASCII format representation. Later, you can move to other more complex formats like .3DS. With this, you not only will understand more how 3D models are saved, you will have to draw it in its raw manner: triangles, and then you will understand how everything is drawn in a graphics engine.
Successfully make your own collision algorithm
It is one thing to draw a world and another thing to manage its geometry. In a 3D world, there are no physics laws, you have to create them. If you want an object not to go through a wall, then you have to create an internal geometric representation of the wall and make all the calculations yourself. There are several approaches to handle collisions; I recommend starting with binary collisions with a labyrinth project. Try this link for more information.
Implement a small particle engine
I was disappointed when I found out that fire, smoke, some lighting and other stunning effects that you see in 3D games are made by particles and that particles are in essence planes with textures facing the camera. The more particles you add, the more realistic the effect looks but the performance is more compromised. The first particle engine I made was a rocket smoke and I did it without looking at a particle engine tutorial. Later I realized I had reinvented the wheel but I was really into this. By carrying out this, you will understand concepts like particle emitters, particle behavior and bill boarding techniques, among others.
Learn the basics in a 3D modeling software
In order to make changes to the 3D models you want to use in your application, you should at least know operations like translating, scaling, rotating, texturing, exporting to other formats and making simple models. If you don't do that, you will suffer from depending on other people to do your first game. I've worked with a few modeling software and I strongly recommend 3D Max or Maya.
Load and play an animation
Loading and correctly playing an animation was the most difficult thing in 3D that I've ever did. I had to do reverse engineering to a 3D max .XAF file. I had to also learn stuff like bone hierarchy, matrix interpolation, among others. At the end, it was very gratifying to look at your own models to move by themselves. I recommend starting animating a robot since models like animals and people require another technique called skinning.
Code a 2D custom Graphic User Interface (GUI)
When I began programming in XNA; I was forced to build my own GUI because XNA does not have implemented any windows controls. This gave me two things, the first one was the ability to make my custom GUI controls and the other one was the understanding of concepts like event handling and event capturing. It is not easy, the most difficult control I have made is a listbox, but once it is made you can use it everywhere.
I am sure when you manage to achieve these ten things, you can say you have the basic knowledge of 3D programming. I wrote this because I spent a lot of work to achieve them and because I would like everyone to have a small guideline when starting in this world. My advice is to start making a small game and to try to adapt them on the go. I think this is the best way because trying to learn all this without the possibility to see it in action is not very motivating. If you liked this small article, you can visit my blog for more stuff like this.