Number one on Google

This is how to explain how Google works to put a site become number one.
If a site (for example site A) has three link FROM other site , and site B has only one link FROM other site, so site A would reach number one and site B would reach number 2 on Google search result.

This is just an explanation I got from a show.

So, based on this explanation, I predict if a site wants to become number one on Google search result, this site must have many link FROM other sites. That's why some people whose have a site or blog want to do 'barter link'.

An interesting phenomenon is I have a blog Buku Islam on http://buku-islam.blogspot.com. A few days ago I tried to search on Google using keyword 'Buku Islam' and this blog was in the position number 10 (or more I forget). But after I create a writing and publish the writing through mailing list, the position now is on number 4. Could this phenomenon be explained using how Google works on the above writing?
Maybe...

So many links mean better position.