I have seen quite a few approaches and it varies a lot depending on the organization. I think the very first thing you should do is ask yourself the question, “What do you want to outsource and why?” If you have clear ideas on your goals for outsourcing (skill gap, cost-saving, process efficiency, and more) and what those tasks are, then you can go into the next step of defining the specifics of what’s being outsourced. This could be an entire person/role, or perhaps just a specific part of an entire process.
A lot of companies usually outsource the stuff they don’t like to do, but sometimes that doesn’t work especially if the task is part of their core business. For example, I’ve worked in the past with a company developing software applications (their core business). We took charge of their e-mail and phone channels for sales and support.If you have specific roles in mind then you can probably get more granular. For example, one project we’re about to take on is tagging financial documents.
The full on-shore role is for accountants, but tedious, manual tasks can be outsourced for efficiency and cost-savings. Overall, a solid, conservative way to start is to take the tasks that can be easily packaged-up and handed-off. This allows your organization to ease into the new setup and get over the initial changes associated with outsourcing.