First of all, you need quality content. That does not neccesarily mean a long boring article about some subject in your niche. For example, a friend of mine has a site with photos. Each page has a photo with a brief description of the subject. Each and every page of the site is indexed. Searchers usually find these pages because they are looking for a photo of the subject. So quality content can not only include articles, but also photos, tools, jokes, discussions, forums, videos, commentaries, advice, FAQs or a myriad of other types of content. Be brutal. If you came to your webpage as a regular visitor, would your page be entertaining and/or informative? Would you find your way around the site easily? Would you stay? And, more importantly for our next point, would you recommend your page to others?
You need incoming links! The best incoming links are what search engines call organic links. What are organic links? It is where someone likes your site, and adds an unsolicited link to your site from their site. Sounds easy? Wrong. Gaining organic links takes a long time if you sit back and wait for others to link to you. There are quicker ways to gain good incoming links which we can't cover here but I can thoroughly recommend this page - 101 Ways to Build Link Popularity in 2006. Of course, all links are not created equal. As a general rule of thumb, links from sites which are more authoritive relevant to your website carry more weight with search engines. Least weight is given to irrelevant links from low ranking sites. To give examples, if I have a site about growing cactus in the UK, a link from the British Cactus and Succulent Society would be an ideal link. A link from a home loan site would be totally irrelevant and would probably be ignored by search engines.
To summarize links, search engines consider links from other pages to your page as a 'vote' for your page, however some votes are better than others. As Andy Hagans and Aaron Wall say on the abovementioned page, "Because links are still the basic connector, the basic relationship, on the Web. And for the forseeable future they're going to be the easiest way for a computer program to judge the importance and trustworthiness of a Web page."
Links from better sites are always harder to get, but if your content is worthwhile major sites will happily link to you. Don't bother with reciprocal links (where someone links to you if you link to them) as these links are usually worthless. The better your incoming links, the deeper search engine crawlers will go into your site and the more pages from your site will get indexed. The better your content, the better your links, the more accessible your pages are, the higher you will rank.
