How to Increase Page Rank
remember, it is pages not sites that have PageRank - so link to specific pages, not just your domain
only indexed pages have PageRank - in other words a link from a page that is not in the Google Index is virtually worthless
don't leave danglers: a dangler is a page on your site that has links pointing to it from external sites but which does not link to other pages on your site. Danglers are wasting PageRank - by internal linking to your other pages you are sharing around the PageRank value (linking does not diminish the value of the linking page but the voting weight is shared amongst all links). Your navigation system can ensure that PageRank is optimised - CSS menus are internal links.
don't get rid of old pages - you will lose the Page Rank. If they are no longer to be part of your website, remove them from your navigation system and add a link from the old pages to the replacement page (using appropriate keywords in the link text). If you move the old pages, the external links will no longer work and you will lose your Page Rank.
seek out pages with high Page Rank. Again, Market Samurai can help you - it will find links at Web 2.0 sites such as Squidoo, Hubpages, Weebly and at blogs and forums. See my guide to obtaining backlinks.
link weight is important
ensure that links to you are "dofollow". Hyperlinks with a rel="nofollow" attribute do not influence the link target's PageRank. (Note: different search engines apply "nofollow" in different ways - check out this Wikipedia nofollow article, in particular the table in the middle of the page.
consider making links to external sites "nofollow". This will prevent Page Rank 'Leakage'. Each page has a certain weight it can pass on. The links from the the page share the weight. So if you are linking to external sites, then you are allowing weight to leave your site and reducing the value of your own internal links.
the sharing of link weight also means that the number of links on a page is important; a link from a high PR page with lots of external links may count for less than a link from a low PR page with few external links.
thematic relevance - there is some debate about how much this counts, but as I said on my SEO Basics page, the key to successful SEO is to try to think like Google. It would seem to make sense that:
a link from a site with similar content should be worth more. A link from gardening site to another gardening site should be weightier than a link from a soccer site.
the content around the page on your site should have a thematic connection - ie more pages that are gardening related links within paragraphs are more valuable than links placed within a list of other links.
links to relevant high PR pages may also have an impact - they reinforce your page's authority (note there are many sites with high PR that consist almost entirely of links to other sites)
ensure that your keywords are used in both the anchor text and the actual link (ie your filename uses the keywords). Thus if I wanted to link to my page on finding niche keywords, that's what the link would look like. Click here links are a complete waste of time! In the original article by the Google founders (referenced at the bottom of this page), they say "anchors often provide more accurate descriptions than the pages themselves ... anchor text can help provide better quality results." Pretty unambiguous - use keywords in your links!
don't waste time link-trading - Google is clever enough to spot reciprocal links and the default position is that such links are related to SEO rather than providing useful content - so the links will be virtually worthless. Your links are also likely to appear on a page stuffed with links to other sites - that means sharing the weight of a page that probably has a low PR (because of lack of content). A link in the context of an article using your keywords, now that is another matter entirely ...
hubs - try to position your site as an authority at the centre of a hub of similar content sites. This is the fundamental principle underpinning the IFM approach.
Now that you have read the fundamental principles, don't forget to visit the guide on How to Get Backlinks.
Page Rank is Not Linear
As a page's Page Rank increases, it becomes more and more difficult to move to the next level. Moving from PR1 to PR2 is relatively easy, whereas moving from PR6 to PR7 will require many, many more links.
Google PageRank Toolbar
The Google Toolbar provides a page rank button. Note that the toolbar PageRank is not the actual PageRank, although, as I have done on this page, people will often speak as though it is. The Toolbar will provide a value of between 0 and 10. The actual Page Rank will be somewhere between 0 and tens of millions (the maximum value will increase as the Google Index increases). The toolbar also lags behind the actual indexing and so your site may actually be doing better than you think.
Don't Get Analysis Paralysis
Focus on your content, build in the keywords, generate quality links - quite simple really.
If you really There is an extremely comprehensive article on Page Rank at this site, together with a Page Rank Calculator.
If you just have to know how it all works, you may wish to read the original paper by Google founders Sergey Brin and Lawrence Page.