Increasing organic traffic to your webpage assumes that people get some useful stuff from your website. It shouldn't be a "one-time" affair, but people should keep referring your website to others or get back to your site for every small purpose.
To make that happen, we can think of a webpage that contains either "subject specific" or "all inclusive" topics. So we can consider the following aspects to meet our purpose.
The Subject Matter
For this, the first thing to be considered is addressing one of the major needs of people, which are the most "searched for" things on the website. For example, Education, Jobs, Matrimonials, Real Estate, Hot Products, Travel etc.
After you choose the subject matter, now you can get various approach to present them before the readers. It can be an informative approach, a buying guide and a page with buying links, it could be a "how to" approach with relevant solutions and so on.
The Right Combination of Links
Your webpage can include all the above or concentrate on any one factor from the above said approaches. But you have to make sure that all the required links are present in your page and they are working perfectly. Whether your webpage is a static or dynamic one, non-working links irritate the visitors and they would prefer not to return ever for their searches.
Observing my own searching habits, I can say, that more a page has got interactivity, the more are the chances of attracting organic traffic. I have even visited a few forum based sites where I go time and again to get my questions answered. Examples of Yahoo Answers and Quora can stand for this, you see.
Reaching Out to People
The Power of Suggestion works. If you can advertise your stuff regularly in prominent places like Facebook, Twitter and other social media sites, there has to be a positive impact on your site with a decent amount of traffic gushing in. But then, that's their first visit. You have to lure them back with the content, which they feel, they were "just looking for".
With all the above working properly and internally linking each other are bound to show the result. But if things don't work drastically in the first round itself, you might have to keep trying with improving each of the aspects and work more hard towards it, without being discouraged.