An easy way to keep a bookmark is to fold the upper-right corner of a book (aka Dog ears)
Is such an action permitted on Shabbos?
Based on Shmirat Shabat Kehilchata Ch: 28, 16, we are allowed to fold papers but not to make toys/games, because in the case of the toys you are making a kli. The previous point (28, 15) deals on the issur of making marks, even with the nail. The example brought is to know where we are in a book.
HaGaon HaRab Mutzafi Shelita says it is not proper to fold pages of Sifre Kodesh. Here is the Lashon:
"The folding of pages is a bad custom and is not proper for holy book."
If during the week it is Asur, it is also on Shabbat.