The Shabbat prohibition of Borer forbids separating items that are mixed together. Thus, if food is mixed together with an inedible substance, one may separate them only if he removes the food ("Ochel") from the inedible substance ("Pesolet"), and not the other way around. And even separating in this fashion is forbidden if the separation does not serve an immediate purpose. Meaning, one may separate the "Ochel" from the "Pesolet" in preparation for a meal that is about to be served, but not for a meal that will be served later in the day.
There is a debate among the Halachic authorities as to whether these restrictions apply to separating Kelim (utensils), as well. For example, if on Shabbat a person’s cutlery is all mixed together, may he separate the utensils into different piles of forks and knives? Clearly, it would be permissible to remove the utensil that one needs for immediate use from a pile of cutlery. The restrictions on separating cutlery will certainly be no stricter than those that apply to separating food, and thus just as one may separate "Ochel" from "Pesolet" for an immediate purpose, similarly, one may separate a utensil needed for immediate use. The question arises, however, as to whether one may separate cutlery for a purpose that is not immediate. For example, if somebody is setting the table on Friday night in preparation for Shabbat lunch, may he separate the utensils to place the forks and knives in their appropriate places on the table?
As mentioned, this issue is subject to debate among the Halachic authorities. The Taz (Rabbi David Halevi Segal, 1586-1667) ruled that the restrictions of Borer apply to utensils, and thus it would be forbidden to separate utensils for a purpose other than immediate use. This is the ruling of the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933), the Kaf Ha’haim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939) and the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909). Others, however, including the Mateh Yehuda (by Rav Yehuda Aya’ash) and the Or Same’ah, maintained that the law of Borer applies only to items that can be actually mixed together. Utensils cannot be mixed the way foods can, as each utensil remains easily identifiable even if it is together in a pile with other utensils. Therefore, according to these authorities, the restrictions of Borer cannot apply to utensils. This is the ruling accepted by Hacham Ovadia Yosef, in his work Yabia Omer, and thus those who wish to act leniently in this regard may do so. Certainly when dealing with large utensils, such as platters, which cannot really be mixed together in a "mixture" like a mixture of different foods, one may be lenient, as no "separating" is entailed at all.
This Halacha applies to books, as well. For example, if the books in the synagogue library are mixed together, the Shamosh may separate them into different piles or arrange them in their proper places on the shelves. Like utensils, books cannot be said to become mixed together into a mixture, and therefore the prohibition of Borer does not apply.
Summary: It is permissible on Shabbat to separate forks and knives that are mixed together. According to some opinions, this is allowed only if one takes the utensil that he needs (rather than moving away the utensils he does not need), and if this is done for immediate use.