What is the Calvinist perspective on regeneration?

When do Calvinists consider an elect person to be regenerate? If it is at birth, then is it odd that someone who is "regenerate" is living in sin, up until the point of faith in Christ? And if it is at a later time, such as at faith in Christ, then how is that faith in Christ prompted in an unregenerate person? I may not fully understand the definition of "regenerate" (and particularly its distinction from "salvation"), so answerers would be kind to also explain that definition from a Calvinist perspective. Note: This question arose out of comments made in this answer .