When a man is at court, all his followers are in favor. 

解释 ( paraphrase )
中国有个神话传说：有一个人修道成了仙，在他快要升天的时候，把修炼用的药喂了他的鸡和狗，鸡和狗也随着他升上了天。
这条谚语比喻：一个人有了权势，同他有关系的人也跟着沾光。

A fairy tale goes like this: A man who had attained the secret of immortality was about to ascend to Heaven. He fed his dogs and chickens with some of the elixir he had used. So the dogs and chickens went up to Heaven together with him.
This proverbs is used metaphorically to mean that when a man rises in the world, all his friends and relations——even the most humble-benefit.

得道：指教徒学到了教义。
         (Originally for a follower of Taoism) to attain the Way.
         (Now) to be in power.

同义词 ( synonym )
一人飞升，仙及鸡犬。

造句 ( example )
正所谓“一人得道，鸡犬升天”，你们家亲戚发达了，你不是也跟着沾光吗？