The number of backlinks or "inbound links" that your website has is one of the most important factors determining your site's search engine ranking, popularity and importance. The key to backlinks is relevancy. Backlinks from authoritative sites on a given topic are highly valuable.
It should also be noted that building too many backlinks over a short period of time can get a website's ranking penalized, and in extreme cases, de-indexed altogether. Backlinks or "inbound links" to your website will gradually build as your site gains traffic and popularity. You can help this along by building backlinks from other websites through various promotional techniques. Slow, steady progress is the key here.
Blog about new content or services - Writing a blog post is a great way to let visitors know that new content is on your website.
Don't forget about offline promotion - Putting effort into offline promotion of your website is just as important as online promotion.
Know about social media sites - Sites like Facebook and Twitter that are built around user interaction and sharing make it easy to create a "buzz" surrounding your site.
Reach out to related communities - Since it is more likely than not that there are websites that have much of the same basic content as yours, or closely related content, opening up communications with these sites can be very beneficial to you.