Is it appropriate for random students to approach professors they admire? I am a freshman, and over the summer I found out about a professor at my university who has recently published a book. Curious, I bought a copy and ended up falling in LOVE with this man's writing. As an aspiring author myself, I would be honored to receive advice from him. 

But would it be too weird for me to go up, introduce myself to him and be like, "Hey, Dr. ___, my name is Jenny. I read your book and loved it. Is there a time we could possibly get together and discuss it? I just have a few questions." 

I'm asking because I'm not sure how common it is for students to do this. I know it would be one thing if I was in his class, but I'm not. Unfortunately, I will not be able to take his class for several years, as he only teaches upper level courses. 

I just don't want to seem annoying to him, or like too much of a fangirl. But like I said, I was mesmerized (cheesy as that sounds) by his book. I thought it was incredible, and I'm dying to talk to him about it. I definitely wouldn't want to sound demanding or anything; I'd ask him if he would be willing, and at what time.
There's nothing wrong with approaching a professor whose work you are interested in and asking for an appointment. The worst that can happen is that the professor will decline to meet with you. However, most professors (like most human beings!) will be appreciative that someone enjoys reading their work, so I'd think you're more likely to find the professor will agree than not.

That said, I would probably change what you'd say. Rather than just say "I have a few questions," I'd say "I'd like to know more about X and Y." This shows that you're serious in your request.