Getting from PR1 to PR2 should generally be easy, given a little dedicated linkbuildning. Having that said however, attempting to improve your PageRank, might not be the best way to spend your time. As for how long it will take, well that generally depends on when the next PageRank update takes place, and whether a page managed to do whatever it takes for that particular page.
Backlinks is not the one and only thing that matters, because other things are also used when calculating PageRank, such as the internal flow on your website. What this means, is that you, to some extent, will be able to sculpt the rank of the pages on your website. This and more, may be covered in Brugbarts SEO Tutorial.