What is the best and cheapest way to improve a specific keyword searches?
I was thinking about if, there is any proven strategy or case, which help improve searches of a specific keyword.
The most effective way of doing this is to write good and relevant content using those keywords over a period of time that gets linked to by the rest of the web.
Content Marketing has become the current buzz word du jour for good reason ;-)
If you can get people to read the content - and it's relevant - they'll come back. And talk about it. And link to it.
SERP rankings are a trailing indicator of success, not a leading one.