If your server is accessible via
http://teamcity:8111/ URL, use:
http://teamcity:8111/httpAuth/api/version - to get plugin version
http://teamcity:8111/httpAuth/api/projects - to get projects list, then follow href's
http://unit-212.labs.intellij.net:8111/httpAuth/api/buildTypes/id:bt284/builds?start=40&count=20 - (example ids are used) to get builds
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.
Builds at buildserver.