Ok. You likely got here by searching in Google for From PR2 to PR3, which could indicate that you are looking into the wrong aspects of SEO. Try not to focus so much at your pagerank, instead we recommend that you start focusing at the bigger picture of your site instead.
See also: Brugbarts SEO Tutorial
It doesn't matter if your site is PR2 or PR3 – you can often achieve higher rankings simply by releasing quality content. However, that is not to say that pagerank doesn't matter – it just might not be the first choice, as of where to focus of your attention.
How Long Does it Take to get From PR2 to PR3
How long it takes depends on a lot of things, but mostly the links pointing back to the page that you want to become a PR3. Your site could become a PR3 overnight if it has met the requirements to do so – this would often mean that it has obtained the required backlinks. If the page has already met the requirements by Google to become a PR3, then you just have to wait for Google to update the toolbar pagerank.
See also: How often is PageRank updated?
It is sometimes said that for your site to obtain a certain pagerank value, it needs to have incoming links from a site with a higher pagerank – that is however not necessarily the case.