You may be able to deduct your moving expenses from your taxes. If you'll be moving to a city with lots of university students, the summer is probably the easiest time to find cheap short-term housing. Check the off-campus housing office at the university in your new home town. You might be able to find a sublet. You can also try living in residence at the local university.
Space is limited, so get in touch with the school early.
Get to know the Landlord and Tenants' Act in your new province or territory. In some provinces, you need to give two months' notice to your landlord before moving. You probably already know that moving and students go together. Make sure you back up your hard drive so you have a spare copy of all those essays and lab results you wrote. Pack the computer in its original packaging, if you still have it.