In the case, of Bryant, it should be fairly straightforward. If you're primarily concerned with modern browsers, something simple like this, added via the CSS Editor, should do the trick:
If you want broader compatibility with older browsers, and if you don't mind some overlap of your header image, you can instead use:
On a related note, on other templates based on Brine (not yours, but others may end up here looking), the number of concerns when creating a fixed header are much greater and include: differences between index and non-index pages, what headers (top/bottom) are enabled, whether the screen is resized, whether the announcement bar is used (and whether it's been closed), whether the header covers up content when anchor links are used, whether you want it fixed on mobile, whether you have the headers set to overlap on index pages, and more. To account for that complexity, I created Fixit - Fixed Headers for Squarespace. In my experience, many tutorials and code snippets fail to take one or more of those into account.
In your case, the above should work. But I say all that in part so that, if you find anomalies in certain contexts (the announcement bar visibility being one of them), they are probably solvable. Just post back and include a link to your site and the view-only password for trial sites.
Finally, custom CSS will be applied even for trial sites.
Hope that helps.