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As stated, workflows in SharePoint are normally human-centric. While the workflow performs some actions like sending an e-mail or updating a list item, the tasks that people do form the core of the workflow design. The other actions are used to keep everything organized and manageable. This workflow, for example, can be distilled down to the following:
You have already implemented the first task, which is to review and approve (or deny) the request. The second task that you'll implement now is to fulfill the request.
SharePoint provides a generic task process that you can use for any human task. The approval task that you just implemented uses an Approval workflow, which is a special case of the generic task process. SharePoint also provides two other workflows based on the generic task: Collect Feedback and Collect Signatures. These work in essentially the same way.