Believe it or not Google wants you to do well in their search engine listings. If you're serious about showing up in Google, they have a whole section of Google oriented suggestions to help you. This page covers some of what they discuss and some additional ideas as well.
Google judges your site not only by how it's constructed and how much content there is on it, but by how many other relevant sites link to it. If you have a relatively narrow topic (e.g., postcard collecting), you may already know most of the sites that are related in topic to your own. Write the webmasters of these sites and suggest an exchange of links. If you think a site will be usefu to your visitors, link to it even if you don't get a reciprocal link. It will make your own site more informative.
The goal of reciprocal linking is to get and provide qualified traffic to and from other websites that complement yours. The process of swapping links is time consuming but worth the effort. You can tell quickly and easily how many "backlinks" your site has by using the link popularity checker above.
Google has caught wise to the exchange of links just for its own sake. If you are going to go to the trouble of exchanging links, make sure they are relevant to the content of your site. Otherwise, Google will discount them!!
Before you start trading links, make sure to download Alexa's free toolbar. Alexa ranks sites by how much traffic they get, so you can judge better whether a site is worth linking to. They also list related sites, so you can get suggestions of similar sites that might want to trade with you.
If you don't necessarily know of sites you want to trade links with, there are categorized directories of websites that trade reciprocal links. LinkMarket.net is one of the biggest. It offers both free and paying memberships. An up and coming link exchange is Zeen. They even build your links page for you. LinkBox.ws - Link Box Exchange offers both free exchanges and paid links.
You can also buy non-reciprocal links. There's a brisk business in buying and selling links at sites like LinkWorth, AdBrite and LinkAdage. If you have time and patience, trading links can be a nice way to get to know some of your competitors and familiarize yourself with similar sites. Some link exchangers are quite generous with their encouragement and expertise. If you don't have the time, you can also hire people like Web Promotioner to build links for you.
Link exchangers prefer you to have a nicely organized links page, clearly locatable from your home page. See the one on this site for an example
A word of warning: some people ask you to put links written in Javascript on your page. Since Javascript only executes when you open the page, search engines don't find these links, so they're not going to increase your PR (Page Rating).
A banner is an ad, usually 468x60 pixels big, like the ones at the bottom of this page. A Banner Exchange allows you to display your ad on other sites in exchange for displaying their ad on yours. In less than a month BannerXchange generated 472 hits for the site you are visiting now at a cost of $0. Please note, however, that hits are NOT the same as visits! Every time you display someone else's banner, that's counted as a "hit".
A variation on this idea is a text link exchange, such as txtswap.com. Some webmasters find text ads to be more effective than banners. You can also use contextual text swaps, such as this one: Links - Text Link Exchange.
If you don't want to put ads on your site, there are websites that will sell you a contextual link on other people's sites. Market Banker sells Google-like text boxes. "Publishers" list their sites and the amount they want, you purchase the ad through Market Banker. Link Adage runs auctions. You pick a site that sounds interesting and then bid on a link.
If you're primarily interested in just getting the number of visitors up, you can
spend a few minutes a day surfing via a Hit Exchange such as Traffic Hoopla. You look at other people's sites and in return they look at yours. This is VERY boring as
almost all the sites are get-rich-quick schemes or other hit exchange sites. BE VERY CAREFUL. Before you
sign up for any of the offers you see, make sure you install a Spyware detection program such as Spybot, which is free, AND a virus protection program such as one of the Kaspersky Anti-Virus Products.
Otherwise, you run a large risk of having your PC infected by unscrupulous people. DO NOT join a
Free For All (FFA) program. They're just an invitation to spammers.
This is a variant on a pay-per-click search engine. You offer people who have websites a commission of your sales, a few dollars per lead, or a few cents per "click" (visitor). Google values non-reciprocal links more highly than link exchanges. You'll pay less per click than Google, but you may get fewer clicks unless a lot of affiliates sign up. One advantage of using affiliates is that it raises the number of sites that link to you, without your having to link back. For example, this site links, as an affiliate, to MyCorporation.com.
Once you have some traffic coming to your site, you can become an affiliate yourself. For example, the Floppybank Affiliate Recruitment Program pays $1.00 for each new publisher that joins and is approved by the network.