Hi,
please see [1] for the REST API documentation that lists the available actions to interact with camunda BPM via HTTP.
The REST API is readily available when you use a prepackaged camunda distribution.
You can invoke the API with any Ajax client you like, such as jQuery or the abstractions provided by angular.js. I would advise you to confer the respective client's documentation on how to perform ajax requests.
There is also a javascript sdk [2] for camunda bpm in development that provides a convenient javascript API to interact with camunda REST resources. As it is still in an early stage, there are no releases yet but you can follow its development. It is planned to be released with camunda BPM 7.2 that is scheduled for around October.
Best regards,
Thorben
[1]
http://docs.camunda.org/latest/api-references/rest/[2]
https://github.com/camunda/camunda-bpm-sdk-js