I assume this would vary based on your province, but the general gist of the process is this:
See your general practitioner, explain your issues, get a referral for psych assessment -> wait on the waiting list, or, if this is urgent (violence or suicide risk) they may triage you to the front of the line -> do the psych assessment interview with a psychiatrist -> depending on the psychiatrist's assessment, you could be referred for neuropsychological testing -> wait on the waiting list for that -> do the testing -> find out exactly what your diagnosis is. If you do it this way, the whole thing should be covered by your basic provincial healthcare, ie, free.
That's the process I went through. I live in Alberta. One Alberta specific thing I didn't mention is the Access Mental Health department. They act as a general intake for all psych patients entering the system. I had to do an interview with them over the phone before doing my official psych assessment.
You will almost always have to go through your family doctor first before seeing a psychiatrist unless you show up at the emergency room in crisis and have a chat with the emergency psych team.