Confucius quote: what's the original? The man who moves a mountain starts by carrying away small stones.

This is (reportedly) a quote from the Analects of Confucius. I have tried looking for 山 in the whole Wikisource text and found the following occurrences:

季氏旅於泰山。子謂冉有曰：「女弗能救歟？」對曰：「不能。」子曰：「嗚呼！曾謂泰山不如林放乎？」三之七
子曰：「臧文仲，居蔡，山節藻梲。何如其知也。」
子謂仲弓曰：「犁牛之子，騂且角；雖欲勿用，山川其舍諸？」
子曰：「知者樂水，仁者樂山。知者動，仁者靜。知者樂，仁者壽。」
子曰：「譬如為山，未成一簣，止，吾止也！譬如平地，雖覆一簣，進，吾往也！」
色斯舉矣，翔而後集。曰：「山梁雌雉，時哉時哉！」子路共之，三嗅而作。
公山弗擾以費畔，召，子欲往。子路不悅，曰：「末之也已，何必公山氏之之也。」子曰：「夫召我者，而豈徒哉？如有用我者，吾其為東周乎！」

None of these seems to match the given translation. So what is this quote? Is it a fake? Or is it really from Confucius, and if so, what is the original? And as an extra, what do these quotes mean?
譬如为山未成一篑 is talking about making a mountain rather than moving a mountain. It tells about the importance of perseverance.

Another Confucian classic, 《荀子》 has 积土成山风雨兴焉 in the article 劝学 meaning you accumulate earth and make a mountain then the local climate will change. Again, the same moral, but not told by Confucius himself. 

Yet another classic but is about Taoism, 《列子》, has an article talking about a silly old ram thought he could punch a hole in a dam -- A silly old man thought he could move a mountain with a 1000 year plan, and eventually he did in his life span, because the Sky God helped his clan. This is, again, all about the same thing, perseverance.

So yes, it is probably fake. At least we can tell it's not from the Analects.

About the meanings of these quotes, you can find the Chinese translation of 论语 here. For more detailed explanations of each quote, google is your friend. Search one of the quotes and you'll get plenty of answers.