First, let me say that PR or PageRank (1 word), is not the same thing as “page rank” (2 words). PageRank, named after Google co-founder Larry Page, is a calculated score based on the Random Surfer Model using a logarithmic scale of 0-10. While “page rank” is generally used to refer to your ranking position in the SERP.
Since your question seems to be asking about how to quickly increase your PageRank score, I will try to answer that. The answer is very simple, yet not very easy to accomplish.
Your PR score is derived from the amount of link juice passed to your page from the web page that links to yours, divided by the number of outbound links from that page, minus a decay factor. The higher the PR of the page that links to yours the more total link juice your page receives.
To increase your page’s PR quickly all you need is a link from a high PR page that has relatively few outbound links. Please note that I said “page”, not “site”. Google does not assign PR to sites, only individual pages.