First let me say that you need not use a gift bag of course. Any thick paper you like will do. But let's assume you are going to recycle a bag you already own for the sake of this article.
Cut the bag open along the seams so that it lays flat. Lay the book in the center of the bag and fold the top over the book, making a crease to mark where the book lies. Do the same with the bottom.
Remove the book and fold the paper bag along the crease marks you just made. You should now have a piece of paper that is long from left to right and is the same height as the book.
Place the book back onto the paper and fold the paper over, matching up the ends. In this step you will be measuring the length of the ends to see if they will need to be trimmed. The long ends of the folded paper should extend beyond the book cover about half the width of the book. For example, if the book measures 10" from left to right (closed, not open) then the paper should extend 5" over the edge of the book both on the front and the back. Trim the paper until this is the case.
*If your paper is naturally a little shorter than this, it will still work, so don't worry.
Now you need to insert the book into the cover. First open the book, then insert the front cover into the flap of extra paper. Repeat this process with the back cover and center the book. If you wish, mark the cover with a crease, remove the book and fold the two flaps to create a sharp line. This will give you a look that is not quite as loose.
Once the book is inserted and you are happy with the fit of the cover, you can tape the flaps so the book does not slip out.
That's it, now you can use your imagination to personalize your book cover.