PageRank is something which I have avoided talking about for most of my work in SEO. The reason for this is quite easy to explain. Every website owner (unless in the know) believes PR is the be all and end all of search ranking, and that it is EVERYTHING Google considers! ... Well I've news... You are Wrong! I asked Matt Cutts ("head of webspam" at Google) - My Tweet to @mattcutts And his response: "not at all" - Matts Tweet
So with this myth dispelled where does this leave the people asking "how do I increase my PageRank?" and saying "I want to increase my PageRank".
Wikipedia defines PageRank as: PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references.
Considering this definition PageRank is a ranking given to websites based upon linking relevance of other sites to your site, not the number of links. Getting links from higher PageRanked sites (of relevance) means your rank will increase more than if you get hundreds of lower PageRanked sites. ... So that's how you increase PageRank....
However, the real question is why would you want to dedicate all of your efforts on PageRank? There isn't a good enough reason to do this from what I see, unless your amongst the majority of people who follow the myth i've dispelled. PageRank should NOT be considered your search rank, for ANY search engine! Proof of this is searching the same terms in Google and other search engines (even something as simple as "cheese" will yield different results!).
In concluding, you should really be able to ignore PageRank (the word page refers to the creator larry page! not web page!). You should be considering search ranking improvements through SEO, Here are my Top 25 Tips for SEO Success.