JSZlib currently just implements the "inflate" part of zlib, but there will hopefully be a port of the "deflate" portion in the future.
JSZlib is based very closely on jzlib (http://www.jcraft.com/jzlib/), and is distributed under the same (BSD-style) license. The author of jzlib, ymnk, in turn credits Jean-loup Gailly and Mark Adler for the original zlib code.
Simplest way is just to call jszlib_uncompress. Takes an ArrayBuffer, returns an ArrayBuffer, throws an exception if something breaks. You can also use a ZStream class which behaves much like ZStream from jzlib. This might be useful if you need to uncompress partial data -- some kinds of streaming network protocol, for instance -- but is overkill for most applications.