Given a positive integer n, how many zero rings exist of order n? Inspired from this question, in this paper, author is mainly concerned to determine the structure of zero rings of a given order; in particular, we tempted to try out the structure of each zero ring of order <= 50. In the course of the investigation, basic properties of zero rings are obtained and the results relevant to the counting of subrings, and ideals for a given zero ring have established.