In Vancouver, Landlords pays for the property tax. You can also check rental listings in www.rentbc.com. If you are interested in any listing, just phone/email the landlord. If the landlord approved you as tenant, they will ask you to sign a tenancy agreement and ask you the money for the first month rent advance payment and half month rent as security deposit. Then you can arrange to pick up the keys.
Downtown is generally more expensive than other areas such as Burnaby, Richmond and Surrey.