I don't think the GRE will be considered at all. Those tests are designed to trim the fat from huge amounts of applications (eg. MBAs)...PhD applicants are easier to trim based on the quality of their previous research, but, more importantly, the quality of their research proposal.

What awsoci described is fairly similar to the process at my university, though mine is less involved (popular g08 university)

First, you need to search through the faculty and try to find all of the researchers who you think might be interested in you based on their interests and publications. From this shortlist, you should try to make contact with them via email, expressing your interest and then go from there (they can usually help bring on a 2nd supervisor).

Then you formally submit your application after being invited to do so...It consists of the following:

1. Brief research proposal (there are many guidance papers on how to write a good proposal, check on SSRN).
2. Officially certified academic transcripts for all tertiary degrees.
3. 2 academic references.
4. Some evidence of research experience ... usually they want to see your thesis examination reports if you have not published.
5. Housekeeping stuff like passport, Q&A stuff etc.

Good luck!