So what you want is, Oh about the equivalent of the first 12 chapters of the book 'Tricks of the 3D Game Programming Gurus' posted here to the forum ... actually, it's not quite that bad, but it's close

Rather than start with an all-in-one post like this, you might find it better to learn in smaller steps:
1, Positioning and rotating a point in 3D space in relation to a viewpoint (ie, the camera)
2, Drawing a line between 2 dots in 3D space
3, Clipping a line to the display
4, Assembling a 3D wireframe object from multiple lines, including clipping
5, Implementing a flat-colour rasteriser to fill your object
6, Implementing a z-buffer to ensure object is rendered correctly.
7, Implementing a gourand-shaded rasteriser to fill your object using vertex colouring (basic interpolation)
8, Implementing a texture rasteriser (interpolating uv coords to get a texture coordinate)
These steps get bigger and harder as you work through them (actually, the jump from step 7 to step 8 isn't too difficult).
Somewhere in there you'll probably want to extend the line clipping to include full object clipping within the viewing frustrum, but that's only (!) a speed optimisation, and you don't need to know it to actually render.