From the All Books view, click into the Collection you want to move the book from. Click on the 3 dots to open the book menu, and from here you can move a book to another Collection in your account.
Also, if you would like to import a book into another Collection, click into the folder.
Click on Import existing book...
Select your book from the drop down list and click add to collection.
You can also choose a collection to save newly created books to. Just select the collection to add it to before you add any coverage!