there are specific areas and times where you can use it. the ones i remember are;
Sarah: in the streets you can give her the book from the menu and she says she'll read it then meets you at your house later.
Julia: talk to her in the library and "cast" book from your portrait in the corner. you can return to the library a few times for scenes and she can give it to Ashley later.
Cassandra: beat her when she challenges you and "cast" the book during the aftermath conversation.
Jane: at the end of a secret note class you have a short window to "cast" the book, this triggers an ending when you return to the classroom.
Reese: I think you can give it to them when you and Cassandra meet them in the woods, but I am not sure when it is an option.
Valerie & Rosa: only shows up when you are Rosa and repeatedly enter your room. eventually you succumb to the book and take Valerie with you.
For the Cass one, you actually need to *lose* to her, and then "cast" the book when she tries to get you to say "Yes, Mistress.", which she'll assume is you giving a gift to avoid needing to say those words out loud.
You can also use it on Angie (the lady who owns the store that Molly works at), by getting molly fired or in the latest update getting her to quit, and then enslaving Angie with the "greedy" path where she's not actually enslaved but is bound to your will, then giving her the book when talking to her in the Shop. This will also snag Molly for you, though not as a proper slave.
You can
also use the book on Brittany, the alien girl who runs the Enchantment Shop.
As for when giving Reese the book is an option, you need to side with Reese in the convo of you meeting them in the woods alongside Cass, and give the Book to them when they demand you make it up to them for the humiliation you've been accidentally putting them through due to Cass' outburst from the Cass+Sarah's Past plotline where Cass got angry about the old wound of Sarah being straight, bought a Sex Change potion, and then was convinced by you not to use it and tossed it into the lake, where it diluted massively and thus made the sex change it caused to Reese irreversible without much stronger magic than what goes into the potions.
You can also give the Book to Mrs. Rack, as long as she's not your slave, at the end of one of her lessons, by "casting" it on the final line of one of those lessons (the one that has a red square to indicate hitting Enter or Space again will send you back to the area navigation (which is the same line point of Jane's classes that you need to cast it for giving it to her)), then walk back into the room and claim her, with the option of telling her to share it with others. Choosing to tell her to share it will nab you Dr. Tiff as well, who you can then tell to share the book with students who come in to be healed by her, with a few scenes for that that will have a random chance to proc whenever you later enter Tiff's classroom/office/clinic.
You can also give it to Erin as one of the methods of enslaving her brother Eric, when she brings up that he's getting suspicious of her different personality, but you need to swap her to Normal or Country Personality before giving it to her after she brings up his suspicion, or else the attempt to Book Eric will fail because he won't trust Erin enough to end up being force fed a Sex Change potion to fall under the Book's influence.
You can also give it to Victoria, via "casting" it from your convo-spell menu when she confronts you about your slaves (she'll end up in your living room, at which point you can officially claim her and retrieve the book for further use on others).
And you can "give" it to Kate, by trying to "cast" it at her when meeting her back on the surface after she rescues you for the first time in the dungeon, though she'll refuse the "gift" claiming that heroism is the only reward she needs.