Great question, because proofing your book is going to ensure that you're happy with the end result. There's a couple of ways you can proofread your book in BookSmart.
Option 1: Print out a proof copy
Select File > Print in BookSmart and print out your book. Note: This won't print your cover, so you'll have to proof that carefully on screen.
Option 2: Proofread on screen
Click the blue Preview Book button in the lower right side of the BookSmart screen.
Carefully review your book
Regardless of which option you take, you'll want to closely read every page of your book. Carefully examine the text for spelling errors and look at the placement to make sure that the text appears where you want it and that nothing is missing or cut off. Be sure your photos look accurate and that no important content is in danger of being trimmed off or lost in the binding.
If you really want to take this up a notch, have someone else give your book a read-through. It helps to have a second pair of eyes review your book.