Skydome is just a sphere drawn around the entire level. Just draw a sphere, make sure that the flipping of the back surface is turned off, and the flipping of the front surface is turned on (since you are inside the sphere).
For procedural creation of a sphere is trivial, my usual approach is to start with hard-coded Icosahedron and split the faces until the required details are reached. There is a thread on the gamedev about creating a sphere: http://www.gamedev.net/community/forums/topic.asp?topic_id=537269
I'm not sure what really answers your question, seeing that your answer to another answer makes me think that there is some kind of confusion about what skydome is. To repeat this is just a sphere, an important bit is the texture that you draw on it.