Overview of the process

Here are the general steps that you'll need to follow in order to become a Permanent Resident (PR):

I. File an application for a Certificat de Selection du Quebec (CSQ) at the Montréal office of the Québec ministry of immigration (MICC):

1. You will need the application itself, supporting forms, documents showing your language skills, certified copies of everything (identity proof, education, work experience etc), proof of status in Quebec and Canada, as well as translations of documents.
2. You will receive an acknowledgment of receipt, followed by instructions to send extra documents (if missing), followed optionally by an invitation for an interview and finishing with the receipt of the CSQ itself.
3. This can last anywhere from 2 to 6 months, with the current average being around 3.5-4 months (from start to finish).
   

II. File an Application for Permanent Residence at the Consulate General in Buffalo, NY:

1. You will need the application itself, supporting forms, documents showing your identity, birth certificate, original police certificates, proof of status in Canada, the CSQ, as well as translations and certified copies of all of documents.
2. Be sure to answer ALL QUESTIONS in the application, even those that do not apply to you (just put "N/A" for those). The Buffalo consulate is known for being very quick at returning incomplete applications.
   
3. You will receive an Acknowledgment of Receipt (AOR), with, perhaps, medical instructions, and information on whether you're required to provide a Canadian RCMP criminal record or whether you are invited for an interview. You might also get an Initial Assessment (IA) which states that your file is complete and is waiting for the background check to complete.
4. Your file might get transferred to another consulate, for speedier processing.
   
5. After the background check is cleared, the medical results are in and everything is in order, you'll get an invitation to pick up the visa or to send in the passport. Be sure to follow the instructions of the particular consulate or embassy, since they are quite picky about the mailing instructions.
6. Complete applications that are in order and that don't require any special treatment (no suspicious background, no severe medical conditions etc) are usually dealt with in 4-8 months at Buffalo, from start to end.
   

III. "Land" at a Canadian Port of Entry. This can either be done by:

1. Going to the US border, entering the US (you might need a visa), making a U-turn and "landing" at the Canadian border. You don't need to go to the US, you can go anywhere else as long as you get out of Canada.
   
2. If and only if you have a work permit valid for at least one year, have been working for at least one year under that permit (in Canada) you can "land" without going out of Canada by going to an office of Citizenship and Immigration Canada (CIC). There's one in Montreal. (This has changed now, anyone can land in Canada if they're already legally in Canada)
   

The sections that describe these steps in more detail also contains references to the statements that I just made.