Ask them How they Felt
Children love expressing themselves and after they have finished reading a book entirely, or just even a few chapters, you should ask them how they feel. Every child will have a different view on what they read, giving you the opportunity to clear any confusion that they may have had if you also read along as well. But instead of reading it aloud to them, allow the children to read it themselves, ultimately building their vocabulary and sharpening their mind.
Would They Want to Read it Again
Asking whether they would want to read the book again will force your child to think for a while and decide whether he/she felt that this book was one that they will like to pick up again and continue reading. This will also give you some insight on what interests your child, allowing you to pick out related categories of books when you go shopping or to the library next time.
If the answer you get is a no, make sure to ask him/her why that is and what is the reason that forces them to leave it alone and not read again. Advocate to your child that reading something again may give them much more as compared to the first time.
What they Liked and Did Not
Asking children about what they liked and why will open up their mind to different concepts of analyzing a situation. They might like a magical creature in a fantasy story, but may not have an answer for why they like it. If you ask them specific questions in this regard, the child will be forced to think what is it that really attracted their mind towards that specific character and not the others as much. It certainly is a great way to spend quality time with your children.