Link Popularity is a measure of how many sites are linking to you, and how important those links are. Also known as backlinks or incoming links.
The best way to increase your popularity ranking with Google, is by having other highly-rated sites linking to your site. Google have named their value "PageRank" or "PR".
Having a high PR does not guarantee you being at the top of results for your targetted searchphrase. Currently Google places a lot of importance on the "link text" used to describe your link as it appears on other sites. And possibly the surrounding text as well. And eventually the theme of the page. So if you want to be ranked well for say the phrase "pink bellies", then ask sites if they will link to your site using the text "pink bellies". Ask a lot of belly sites. To avoid being considered as spam by Google, slightly vary your link text, for example "pink belly" "belly in pink".
The ideal situation is that your site is just SO valuable, that other sites will link to you as a reference. Failing that, they may link to you if you reciprocate by giving them a link. Choose sites on related subjects, with not too many links per page, organised by theme, and hopefully with PR.
A fantastic free method for finding valuable related sites who are happy to exchange targetted links, is Sitesells Value Exchange. You register your domain and the subject of interest, and they will mail you periodically with a list of sites suitable for link exchange. And it's completely free.
SiteSell also has a search tool that includes searching for related sites, directories, keywords and backlinks. Check it out at SearchIt.
Brad Callen has created a solid tool for finding and managing links to your site, called SEOElite. It allows you to find high-PR related sites, automatically email them, find who is not reciprocating links, manage potential partners, and much more.
A slow and steady method to find sites to exchange links with is to search on Google, MSN or AltaVista for the top results for your chosen keywords and ask if they will link to you. Even though they are your competitors. Hopeflly your site is jst so much better than theirs that they are not a threat to you. With your unique selling proposition (USP). Then find out who is linking to those sites, by typing the LINK command. If those sites have a page where you can link to, exchange links. Google is famous for not showing ALL incoming links. Altavista and MSN are good for searching for incoming links.
From experience, many people say they will exchange, but never place your link on their site. So at the end of each month, check your site for incoming links, and delete references to those who are not, preferably after giving a courtesy warning notice.
A quick way of finding sites willing to exchange links, is to include extra words in your search. For example search on Google for "home business - add url" to find willing partners for the home business area.
Sometimes you strike it rich, and find a quality site who only exchanges with other quality sites. Examine who they have linked with, and approach those sites as well. Assuming, of course, that you also have a quality site with only quality links.
These days, as so many people do not reply to emails, I am starting to send an inquiring email first, and only adding the link after their response. It seems to be accepted practise on many forums.
Get your site mentioned in as many places as you can. Other tips to improve your ranking:
Find out whether you are indexed, your link popularity and saturation using free tools at these sites:
AddMe
MarketLeap
TrafficRanking
Link Popularity
Link Popularity Check - Checks MSN, Lycos, Altavista
Find sites to exchange links with you:
Links To You
EProfitNews
LinkPartners
If you'd like to learn more about link building, check out LinkingMatters.com and Linking101.com
Search engines are always trying to improve the efficiency of their algorithms, to provide better results for the user. Engines like Teoma and AskJeeves value an incoming link from a related subject site higher than an unrelated link.
If you have money to spare, you can buy tools to organise your links for you, eg:
LinksManager. Although purists say that a manually managed link directory is best, because you can vet your link partners.
Although there are many free link checking tools that you can download to see if your links are valid, and reciprocated. Although you will need to maintain the reciprocal link information.