1. Find the apartment you like with ease (by checking multiple websites). 
2. Call the landlord and schedule a time to see it. Weekends and evenings are normal and preferred visiting times.
3. Decide you like the apartment and tell them you want to apply.
4. Provide your SIN number so they can do a credit cheque, fill out an application (stating what you do), show some proof that you are working, give a cheque for the last month's rent as your deposit.
5. Live in apartment. 

This is the way apartment renting SHOULD be. Please see my post about renting an apartment in Rio without killing yourself.

Sometimes I have to admit that I am super grateful we are in Canada.