It is built on API introduced in Weblate 2.6 and still being in development. Several commands from wlc will not work properly if executed against Weblate 2.6, first fully supported version will be 2.7 (current git is okay as well, it is now running on both demo and hosting servers).
How to use it? First you will probably want to store the credentials, so that your requests are authenticated (you can do unauthenticated requests as well, but obviously only read only and on public objects), so lets create
[weblate] url = https://hosted.weblate.org/api/ [keys] https://hosted.weblate.org/api/ = APIKEY
Now you can do basic commands:
$ wlc show weblate/master/cs ... last_author: Michal Čihař last_change: 2016-05-13T15:59:25 revision: 62f038bb0bfe360494fb8dee30fd9d34133a8663 share_url: https://hosted.weblate.org/engage/weblate/cs/ total: 1361 total_words: 6144 translate_url: https://hosted.weblate.org/translate/weblate/master/cs/ translated: 1361 translated_percent: 100.0 translated_words: 6144 url: https://hosted.weblate.org/api/translations/weblate/master/cs/ web_url: https://hosted.weblate.org/projects/weblate/master/cs/
You can find more examples in wlc documentation.