There are a number of ways. Some of them are:-
Join forums and place links to your site(s) in your signature line. Use your main searchterms as the link text - I'll come to why that is necessary later in this article. But before spending time writing lots of posts with your signature line in each post, make sure that the forum is spiderable by checking the robots.txt file, and make sure that non-members don't have session IDs in the URLs. Also make sure that links in signature lines are not hidden from spiders (view the source code to make sure that signature links are in plain HTML format and not in Javascript).
There you can find a categorized directory of websites that also want to exchange links. Be careful not to sign up with FFA (Free For All) sites because they are mostly email address gatherers and you can expect a sudden increase in email spam soon after you sign up. Also, only sign up with centers where you can approach other sites personally, and where they can approach you personally.
Do not join any link farms!!! Link farms, such as amiztech.com, sound excellent for building up linkpop and PageRank, but search engines (Google in particular) disapprove of them as blatant attempts to manipulate the rankings and they will penalize sites that use them. Once a site has been penalized, it is very difficult to get the penalty lifted, so avoid all link farms.
(a) Search on Google for your main searchterms and find the websites that are competing with you.
(b) Search on Google for websites that are related to your site's topic, but not direct competitors, and ask them for a link exchange.
There are websites that want to sell links. They are usually medium to high PageRank sites, and often the link will be placed on multiple pages, or all pages within the site. It's possible to approach individual sites where you would like your links to appear, but it is much quicker, easier and more reliable to use a middle-man service (or broker).
Link brokers offer links for sale on behalf of other websites (you could use the service to sell links on your site!). With these services, it is usual to be able to choose the type (topic) of the website(s) where you want to place your links. I am not aware of any disreputable practises with link brokering. However, I can recommend the Text Link Brokerage service (banners on this page) as being highly reputable.
Finally, there are even links for sale by public auction, such as the one at LinkAdage Auctions.