First of all in free gallery version you have two youtube gallery modes. You can use youtube links for every image of grid gallery, polaroid gallery, masonry gallery, mosaic gallery or wall style gallery. Every image in media manager have additional options where you can specify youtube video link.
Another option it’s creation of the youtube type gallery (available even in free gallery version). In youtube type gallery you can use multiply video id’s in list to create youtube gallery video right from the videos. In this case you don’t need to upload any image to the gallery galelry just preload previews of every video from the youtube.
In extended version you can load youtube playlists and youtube channels in youtube gallery type. Just in few clicks you can load full playlist of the youtube channel.
All youtube galleries support customization of the interface settings. You can modify gallery hover , videos title or description directly in admin section / youtube gallery / interface settings.
For the first type of the youtube gallery with direct links in images options you don’t need to setup youtube API. In the case of selection youtube gallery type for the case with videos by ID, youtube channel or youtube playlist you need to add google / youtube API into gallery general admin settings section.
Link to the official google guide for the Youtube api setup you can find in admin section.