Rendering works by projecting 3-dimensional objects to a 2-dimensional plane, so they can be displayed on a screen. In modern OpenGL the 3D objects are read from Vertex Buffer Objects (VBO) and the resulting image is written to a framebuffer. This page will cover the pipeline operations involved between input and output.
Some of the steps involved are fully programmable (namely: Vertex, Geometry and Fragment Shader) while the rest is hardwired. However even the hardwired logic can be manipulated by setting OpenGL's state machine's toggles, which are shown in the diagram and described in detail in the OpenGL specification.
In order to begin drawing, A Vertex and Fragment Shader are required and OpenGL must know about the 3D object, which is done by using VBO (and optionally VAO).
The Vertex Shader is responsible for transforming each Vertex from Object Coordinates into Clip Coordinates.
The primitive assembly will use the resulting Clip Coordinates to create geometric primitives, which are then divided by the vertex' w-component (perspective divide) and clipped against the [-1.0..+1.0] range of normalized device-coordinate space (NDC).
As a final step, the viewport application will offset&scale the normalized device-coordinates to window coordinates.
The resulting transformed geometric primitive types can now be rasterized into fragments. Each fragment receives interpolated vertex shader data from the primitive it belongs to, which is at least position and depth. The fragment shader's output must be either gl_FragColor, gl_FragData or set by GL.BindFragDataLocation(). This output is called a "fragment", which is a candidate to become a pixel in the framebuffer. Before this can happen, the fragment muss pass a series of tests called the Fragment Operations.
There is one noteworthy special case found in some modern hardware. The functionality is called "Early-Z" or "HyperZ". After rasterization of the primitive, the resulting Z is used to discard fragments even before the fragment shader is executed. This functionality is not exposed to OpenGL and works behind the scenes. In the diagram to the left, it would belong between the Triangle, Line or Point rasterization, and the fragment shader.
Also note: This diagram targets the OpenGL 3.2 pipeline, but contains a few commands which belong to the ARB_compatibility extension and may be unavailable.