I think if you implement proper search engine optimization techniques, that's fairly achievable. Unless you pay big bucks for companies to do them for you. =)
It will depend on: - The amount of competition for the keywords. - Your niche. - Uniqueness of content. You should have a read over here, its sure a good start - search engine optimization.
It is not that easy and you will never get good results within a very short time period. You have to know about your competitors and have to do lots of quality works to get there.
You need to follow proper SEO for your blog. You need to get good quality backlinks, and you should update your blog daily. don't let your blog in google sandbox.
You can't achieve Google first position within one month. What about your OnPage SEO? Please share your URL.
You can get to first page. You have do quality work. Depends On: - Number of competitor - Quality Page - Quality Back Links
That's not true, it is possible to achieve it #1 in a month. There are a few factors that need to be in place (some mentioned in this thread) for it to happen but it is possible.