I use the quick method for collecting gst/qst, how do I claim my expenses, with or without the taxes?

If you are using the quick method, you calculate everything with the GST (income and expenses). The GST you remit in the year you remit is also an expense for that year.

Really I didn't know that.where would I enter the amount as an expense?

If this is for a business and you are filling out the business form T2125, the taxes will go in Line 8760 "Business tax, fees, licences, dues, memberships, and subscriptions"