Hi,
after you receive the nomination you have 6 months to apply for PR.
In order to apply for PR, as your nomination letter states, you need to apply through the paper based application.
Here is the link:
https://www.canada.ca/en/immigration-refugees-citizenship/services/immigrate-canada/provincial-nominees/application-process/paper.html
Please notice that you have already completed step 1 (which is the provincial nomination), so follow steps from number 2.
From July, if you are an outland application (applying outside canada), and if you are from Europe, Asia you need to give your biometrics. However everything is explianed in the link above.
Regarding the time required to get PR it varies. Up to know the processing times are 19 months and it consists of different steps:
1) Send your complete PR-paper based application to the Visa office stated in your nomination letter. I suggest do it by courier where the signature of the person who receives the package is required. In this way you know for sure that your package arrived.
2) Wait for an email by CIC stating that they received your application and the review process has started. NOTE: it will take 3-4 MONTHS form the time you send the package by mail to the time they send you the email. So need to be patient and wait. When you receive the email that confirms that your application process is started they will give you the APPLICATION NUMBER. This is called as "AOR received" in the various forum
3) Link your application online using the application number CIC sent you by email it is like EPXXXXXXX
4) Now online you can check the status and if there is any request from CIC you will receive an email
5) Wait for the Medical request email. Usually it takes 3-4 months after they send the application number, but right now there is a delay. Indeed people with AOR in March are still waiting for MR (Medical request).
6) after MR it will take another 2-3 months to switch to MP (Medical Passed)
7) Background checks will be ran (not too sure about the timeline here)
8) Pre-arrival letter
9) PPR (request for the passport).
Regarding the last steps (8-9) I am not totally sure because in here not many people reached that step yet so my info are very limited.
This are my timeline, so you can have an idea: (From the OINP application up to now):
OINP under PhD stream, Inland application
Submitted to OINP: Feb 9th, 2018
Assessment: March 15th, 2018
Decision In Progress: April 19th, 2018 (26 calendar days passed from Assessment to DIP)
Approved: May 8th, 2018
Sent to CIC: May 30th, 2018
Received by CIC: May 31st, 2018
AOR received: Aug 2nd, 2018 (CIC sent an email with instructions to link online)
Waiting for MR
I hope this helps