The API is the JMX API that ActiveMQ exposes.
For practical examples you can try using hawtio (http://hawt.io/) in ActiveMQ and then use (if you use chrome but other browsers may have plugins) right click -> Inspect Element -> Network. Then you can see all the network access and thus the HTTP GET/POST that hawtio does to access jolokia to grab the data / do the operations.
Notice hawtio comes out of the box in ActiveMQ 5.9, so its easy to get started with.