This is the official book for learning and using Realm.
Read about the motivation behind Realm, and start with the tutorial: Quick Start Tutorial.
Realm is under active development and should be considered alpha software. Right now there are a lot of API breaking changes on regular basis.
Realm is being used in production at Acko and fifthtry.
PS: You can follow the development of realm here.
PS: If you are planning to use Realm, please post a comment on this issue: get your shit together.