Building decent backlinks to your site can be one of the most important strategies in gaining awareness, in relation to sites of your circle, higher rankings and crucially, long term respect from the search engines.
The links you build should be on relevant higher ranking sites and not on link farms or useless directories. Relevant directory listings can definitely be a bonus but don't focus too much on them, though stuff like DMOZ, Yahoo directory listings can be valuable.
So, how do you go about getting backlinks? Well you can either pay for them or ask politely for a free link, simple as that. Just get a list of relevant sites to yours and ones which are at least... PR3 depending on your own pagerank, but then again, a backlink is a backlink, so just get a decent list of relevant sites to begin.
Once you have a good list, go to each of these sites, find the contact page or find another way to find out who owns the site and email the webmaster asking for a link. Just say that you like their site and ask politely if they wouldn't mind linking to you as you're another good resource for that topic.
Now some people don't just give away links willy nilly so you might end up in 1 of 4 scenarios, either
A: You get a response saying that they will link to you... (perfect!).
B: You get a response asking for a reciprocal link.
C: You get a response asking for payment for a placement.
D: You get a straight... no.
So if you get a straight up yes, that's perfect; you've just gotten yourself a free backlink.
If you get a reply asking for a return link... alot of people would say reciprocal links are pointless and cancel each other out... well, I'm not sure they entirely do but even if they do, depending on the traffic to the apposing site - it still may create a tiny bit more awareness / traffic to your site, so I would say it's worth it. It surely can't do any harm, so why not.
If you get a reply stating that he / she / they do not give out free backlinks and it will cost to have a link placed, ask how much, if they haven't said so already.
Then evaluate if it's worth it, go find out what sort of prices links are going for on certain PR's and if it's even worth buying one on this site. Find out the sites traffic, age, rankings etc.
If you get a straight no then try replying back asking why, if they give no reason -maybe they just didn't want to give out a free link, in which case either offer a return link or a payment (if it's worth it).
Also, when asking for backlinks it's important to get good anchor text. It's been proven that anchor text links are pretty valuable long term these days on the web so you should get in there now. You should vary the text in which you ask your link to be named each time, but not so much and so broad that it could be mistaken as spam. Too much of exactly the same text could also be wrongly taken as inerlinking or cheating by the search engines so make sure you get good healthy text links, but not overloaded.
Say for example you own a website about sleeping problems, get a few links with the text Can't Sleep? or something like that, maybe some with the text Sleeping Problems and then one or two with your actual site title.
A good cycle of healthy anchor text links should help remind Google etc that the backlinks are genuine.