Unfortunately, there is no formal manual for CELT yet. However, you can find some information about it:
The CELT API Reference Manual provides information on programming with libcelt.
The first paper describes version 0.3.2 of the codec, while the second describe the low-complexity mode of version 0.5.1. While there are minor differences with the current version (mostly with the bit allocation), most of the paper is still valid.