If a book that you are interested in is not currently available, you can place a hold on it by tapping the "Place Hold" link to the right of the book image:
That will take you to the following screen where you have to confirm the hold by tapping the big pink "Place Hold!" button:
The following screen confirms your hold, and gives you the option to read a sample of the book, return to browsing, or suspend your hold, in case you want it to come later:
To view what items you have on hold and see how long you have left to wait, go to your shelf and select the Holds option near the top.
On the holds page you can see your estimated wait time, and you have the option to manage your hold.
Tapping the listed wait time will bring up a screen that shows you how many copies of the book the library owns, and where you are in line. If you have cards at other libraries that you have added to your Libby app, this will also show you whether your other libraries own copies of this ebook.
Or, tapping the "Manage Hold" option will bring you to the following screen, where you can suspend the hold (in case it looks like it will be ready soon, but you are not quite ready for it), or you can cancel the hold:
When your hold is ready, the Libby app will send a notification to your phone to let you know that the book is ready to check out.