Basically I bend the spine. This is harder then it sounds.
(Obviously do all your scanning of the covers of the book before bending it.)
Usually book's spine stiff and brittle. Bending it by force would break it. Sometimes literally crack it in the middle.
Solution is obvious. To bend the spine very little from several places multiple times. Here's my method.
I place the book to my hands so that my thumbs are on the spine pressing it (I recommend to keep your thumb's nail short), and the spine is facing me. Then I use rest of the fingers to open the book or press just the middle finger to spine to wedge it more open. Then repeat that process on that book hundreds of times.
I usually make one bend in 5-10 seconds and making book's spine bendy takes from me from 15 minutes to an hour or longer. So we are indeed speaking about hundreds of bends here. The way this is possible is by keeping my hands relaxed and doing it from muscle memory.
Hardest part is to keep spine from breaking. If you use too much force at once, spine breaks and makes further bending far more difficult. But if you don't use enough force, you just waste your time without really effecting spine.
First let's set the terminology.
This book is bendy:
And this book is stiff:
Let's run stiff book trough the first round of bending.
Stages 1-4 can be done by pressing spine with your thumb. (Use both hands)
But after that different method is needed to be able to bend spine more. Turn the book inside out and press and proceed as previously.
Each of the steps can take from 5 minutes to half an hour. It varies hugely between books.
In the latter case, it perhaps makes more sense for you to take the book only to stage 4 or close to it and then just break the spine from as many places as possible. (usually 2 or 3 breaks)
So what the damage to spine from all of this? If done properly, very small.
Sadly that is rather redundant since the damage from scanning will be far more noticeable due having to press the book from it's spine hard against the scanner 100 times (or 200 if you scan single page at the time.)