The other day I was asked how to tell grain direction in a paper you aren’t familiar with. Why the need to know paper grain direction? Well if you are a book binder you want to fold the paper you use for your text pages WITH THE GRAIN. They will fold better this way and you won't be cracking and re-cracking the fibers every time you turn over a page. Additionally, when you make a casebound book you are gluing several materials together and you want the grain of all those materials (the binder's board, the decorative paper for the cover, the decorative paper for the endsheets, the text paper, and the bookcloth) to ALL run parallel with the spine direction. Otherwise you end up getting some interesting warping issues which can pull the book structure apart.
Note: I have dealt with the practicalities of tearing down paper with the grain in a number of posts. I mention one below. Another post you might want to read is Adventures in Bookbinding: Matching Surfaces across Spreads. In that post I show a tear diagram. Along with the other notes I suggest below that you keep, I recommend that you make a tear diagram for every sheet of paper in the way you use it for your favorite sizes of books. You might have 3 tear diagrams for one sheet of paper because you love to use that paper so much in different ways. Having these diagrams will save you time when you are thinking about the size book you want to make and the possibilities of making that book with a given paper.
Now that you know it's important for a bookbinder to know the grain direction of a sheet of paper, it's good to know there are a number of ways to determine grain direction. The easiest is to read the manufacturer’s specs on the paper. Most paper stores will have brochures from the companies. These brochures will list these specs and the store staff can help you with these questions. (Another reason to go to an independent art store that keeps this material handy.) Sometimes catalogs will mention grain direction because some customer has convinced them it's useful.
But if you have done what you can for research and still don’t know there are a couple tests you can do to determine grain direction. Here are some suggestions: