Amazon payments has a strict list of requirements including having a US EIN or SSN, a state driver's license and US residency. Google Checkout is not yet available in Canada.
What are the steps that a Canadian business has to go through to be able to offer these payment processing options?
Get a US EIN. Simple, no?
Seriously, both Amazon and Google are US firms and as such are required to submit 1099 for any payments they send out (with various exclusions for various cases, but being foreign entity is not a valid reason for exclusion). To send 1099 (to the IRS, of course), the payee ITIN is required. That is the SSN/EIN.
To get one your company can qualify as a foreign entity in one of the US states (preferably one that won't charge taxes from your income, Delaware or Wyoming for example), and sign up for a EIN with the IRS. That will also require from you sending out yearly tax reports to the IRS (with taxes due on the US-sourced income, i.e.: all the income you get through Amazon). That might be a bit costly, depending on your business structure, but doable.
Get a professional legal and tax advice when you're going that direction, of course.
I have helped dozens of foreign clients establish businesses here in the US.
You can easily form a corporation or LLC here and obtain an EIN. However, I know of no way for you to claim residency or obtain a driver's license if you don't reside here. Perhaps you can find a trustworthy US accountant to serve as CFO of your US entity - though there are risks and costs associated with that approach.
Disclaimer: This information does not constitute legal advice and does not establish an attorney-client relationship.