Adding third-party ebooks to Apple Books or one of the other ebook apps on your iDevice used to be quite painful. You had to use one of Apple's proprietary cables to connect your iPhone or iPad with a PC and sync the ebooks between the iTunes “Books” folder and the app.
I found it very frustrating every time I connected a device to iTunes, so much so that I rarely bothered. Syncing was slow (it still is) and when the process was finished, app icons were usually scattered hither and thither. It was such a pain that I usually didn't bother.
Fortunately, Apple has long since followed Amazon's lead in making it easy to transfer ebooks to your iDevice.
Here are a few ways you can do that.
You can send yourself an email with the ebook attached, and then open the message in Gmail or another email client. If you click on the attachment, your options will include opening the ebook in an app.
Here's what that looks like for a MOBI ebook attached to a message in Gmail.
Dropbox / cloud storage
If you have a Dropbox account, and you have the app installed on your iDevice, you can upload the ebook to Dropbox and then use the app to download it and open it on your iDevice. Originally this really only worked with PDFs, but in a latest update Dropbox added the ability to open documents in third-party apps.
AirDrop is Apple's feature for letting iDevice owners wirelessly share their photos, videos, documents, and more with other Apple devices that are nearby. You'll need to have Wifi and BT enabled on both devices, and you'll need to be in close proximity for it to work.
Apple has a complete set of instructions on their site.
Send to Kindle
Many companies are catching up to Amazon in making their systems as easy to use, but the retailer still has a few tricks up their sleeves. For example, Amazon lets you send docs and ebooks to your Kindle or your Kindle iOS and Android apps. It is called Send to Kindle, and you can actually email an ebook to your Kindle app on your iPad, or use an Android/OSX/Windows app to o so
I don't use this much on the iPad, but I use it all the times to load ebooks on to my Kindle Fire. (What can I say, it's much easier than using a USB cable).
Amazon has compete instructions on their site.