I have not found a tutorial specifically for mini-panels, but it works similarly to page panels. nodeone.se has an excellent tutorial on using Page Panels (Page Manager & Panels modules enabled).
Mini Panels are closely related , but behave more like blocks. When you define a mini-panel it will be available in the panels UI for placement as well as in the admin/structures/blocks form. The major difference from blocks is that mini-panels are smart. They can take context from the node, user and other sources and display accordingly. They also connect to a View.
There is one thing to observe when defining a mini-panel. The UI is slightly different from Page Panels and the first time I used them, I could not figure out how to add content to one. To access the "content" and other setting forms select the Panels breadcrumb menu at the top.