There are two ways your record can be checked: one is quick, but not always reliable. The other takes some time but is more accurate.
Criminal records in Canada are contained in the CPIC system. The system is nationwide and is maintained by the RCMP, but is utilized by all local law enforcement. The first, and easy method to check your record involves a search based on name and date of birth. In order to have this done, you must go to your local law enforcement office. Depending on what the purpose of the records check is, a name check may be sufficient, and they should be able to do it on the spot.
However, names can be common, people use aliases, etc...so a simple name check will not get you the most reliable evidence. In this case, an application with a full set of fingerprints must be submitted to the RCMP. The fingerprints must be taken by local law enforcement, or, depending on the circumstances, an approved private agency. The instructions for doing this and the fees involved can be found at the following site:
http://www.rcmp-grc.gc.ca/crimrec/finger2_e.htm
This will get you a certified statement of your recrod (or lack thereof), but according to the RCMP's site will take more than 6 months to process.