Adding EPUBs & PDFs to iBooks App for iPhone or iPad

Have the EPUB somewhere on your computer where you can navigate to it. This may require downloading it from an external source.

In iTunes, select the file menu, File > Add to Library

This then opens up the Add To Library navigation box:

Select and Choose the Title you wish to add.

Now be sure the Books > Sync Books setting for your iPhone / iPad is either set to All Books or Selected Books with the title you wish to have on that device selected.

Now, Sync your iPhone / iPad