Examples are excellent learning aids. The following projects implementing JSON API are divided into server- and client-side. The server-side is further divided by implementation language. If you'd like your project listed, send a Pull Request.
ember-data is one of the original exemplar implementations. There is a custom adapter to support json-api.
ActiveModel::Serializers is one of the original exemplar implementations, but is slightly out of date at the moment.
JsonApiClient attempts to give you a query building framework that is easy to understand (similar to ActiveRecord scopes)
The rabl wiki has a page describing how to emit conformant JSON.
RestPack::Serializer implements the read elements of json-api. It also supports paging and side-loading.
Hyp is a library for creating json-api responses.
json-patch implementation of JSON Patch (rfc6902)