Couple tips to getting to the "top" of the pile when applying for an oil rig industry job:
1) Take a H2S course. This course is a prerequisite for 99% of the jobs in the oil industry. The course is a usually held over a weekend and will cost less then $200. Check out "Safety Training" in the Edmonton yellow pages.
2) Take a Standard First Aid course. Again, is often mentioned as a prereq for any oil industry job.
3) One more course is "Confined Space". This one is not often a prereq but will help you understand the environment that you will be working with and around.
If you have a class 1 drivers license, it will help you.....but most places will ask for the first two courses that I mentioned. Once you have these courses, start sending your resume to various oil company websites.
One place to check out for additional courses and information on the oil industry is:
http://www.enform.ca/