If your server is accessible via
http://teamcity:8111/ URL, use:
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/application.wadl to the get list of supported requests and names of parameters.
As a rule, single value responses are "text/plain" and complex value responses support both "application/xml" and "application/json". Supply appropriate "Accept" header in the request to get necessary response type.