If your server is accessible via
http://teamcity:8111/ URL, use:
http://teamcity:8111/httpAuth/app/rest/application.wadl - to the get list of supported requests and names of parameters. Provide valid TeamCity username and password with the request as BASIC HTTP authentication.
http://teamcity:8111/httpAuth/app/rest/version - to get plugin version
http://teamcity:8111/httpAuth/app/rest/projects - to get projects list, then follow href's
http://teamcity:8111/httpAuth/app/rest/buildTypes/id:bt284/builds?status=SUCCESS&tag=EAP - (example ids are used) to get builds
http://teamcity:8111/httpAuth/app/rest/changes?buildType=id:bt133&sinceChange=id:24234 - (example ids are used) to get all the changes in build configuration since the change identified by id.