I've come up with a unique way to give tourists their pictures. It's a specific workflow that utilizes properties specific to the Microsoft Surface 3 tablet. I am certain that the steps of my process have never been combined to provide the service I plan to offer. Since the Surface is a relatively new product, and I don't think anyone's used a tablet in exactly the same way, do I stand a chance of getting a patent?
Yes, you can patent a specific process like a workflow. But in your case there are three potential stumbling blocks: one legal, one practical, and one economic.
Legal: you can only patent a nonobvious process, so stringing together conventional activities into a workflow would likely be insufficient to receive a patent. Novelty ("the steps of my process have never been combined to provide the service I plan to offer") is not enough, in and of itself, to be rewarded with a right to exclude others; it has to be nonobvious too. See 35 U.S.C. § 103(a). Knowing whether something is nonobvious is a very factually intensive process and depends on the specific steps you're attempting to protect.
Practical: the backlog in reviewing patent applications is so long (3+ years) that by the time any patent you filed was granted the Microsoft Surface 3 tablet would likely be obsolete. Filing applications covering processes that will only be relevant for a short period of time greatly reduces the value of any patent you receive. See "Average Pendency of US Patent Applications."
Economic: filing for, obtaining, and leveraging a patent is extraordinarily expensive. Even an extremely simple invention such as a coat hanger could cost $5,000 to $7,000 in attorneys fees to obtain a patent. See The Cost of Obtaining a Patent in the US. You would be in a better position to know the value of your invention, but most patents are worth less than $10,000, which in many cases means it costs more to obtain them than they're worth once granted. See "A Patent Is Worth Having, Right? Well, Maybe Not."
A method or process can indeed be patented. As for whether your workflow in particular is patent-eligible, that would depend on the details of the workflow and how it is claimed, as you'll discover during the patent prosecution process.